Communications in Nonlinear Science and Numerical Simulation, 2010
A new type of linear observer based projective, projective anticipating and projective lag synchr... more A new type of linear observer based projective, projective anticipating and projective lag synchronization of time-delayed Rössler system is studied. Along with this, the approach arbitrarily scales a drive system attractor and hence a similar chaotic attractor of any desired scale can be realized with the help of a synchronizing scaling factor. A scalar synchronizing output is considered where the output equation includes both the delay and non-delay terms of the nonlinear function. The condition for synchronization is derived analytically and the values of the coupling parameters are obtained. Analytical results are verified through numerical investigation and the effect of modulated time delay in the method is discussed. An important aspect of this method is that it does not require the computation of conditional Lyapunov exponents for the verification of synchronization.
Nonlinear processes in magnetized plasma are very much important for the proper understanding of ... more Nonlinear processes in magnetized plasma are very much important for the proper understanding of many space and astrophysical events. One of the most important type of study has been done in the domain of Alfven waves. Here we show that a Galerkin type approximation of the DNLS (Derivative Nonlinear Schrödinger) equation describing such wave propagation leads to a new type of nonlinear dynamical systems, very much rich in chaotic properties. Starting with the detailed analysis of fixed points and stability zones we make an in depth study of the unstable periodic orbits, which span the whole attractor. Next the birth of a Hopf bifurcation is identified and normal form, limit cycle analyzed. In the course of our study the detailed structure of the attractor is analyzed. A possibility of internal crisis is also indicated. These results will help in the choice of the plasma parameters for the actual physical situation.
Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is in... more Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is investigated. We propose an adaptive method that can estimate all the parameters of the response system using the driving signal only. In the past few years, various methods have been developed for estimation of multiparameters of a chaotic system but most of them require more than one time series to estimate all the parameters of a chaotic or hyperchaotic system. The proposed method requires only a single chaotic time series to estimate all the parameters. A sufficient condition for synchronization is derived and it is shown that the numerical results well support the analytic calculations. The synchronized system has applications in cryptographic encoding for digital and analog signals, which is shown with an example.
When two different chaotic oscillators are coupled, generalized synchronization can occur. It may... more When two different chaotic oscillators are coupled, generalized synchronization can occur. It may imply a very complicated relation between the states of drive and response systems. We propose a method that can be used to detect and characterize the generalized synchronization in modulated time-delayed systems. Using Krasovskii–Lyapunov theory, sufficient condition for generalized synchronization is derived. The proposed technique has been applied to synchronize prototype and Ikeda models by numerical simulation.
In this letter we consider a prototype model which is described as an autonomous continuous time ... more In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization phenomenon is examined both numerically and analytically using the Krasovskii-Lyapunov functions. We have applied adaptive coupling law for synchronization,where the coupling equation also contains delay with modulated time. We also studied the effect of cryptography for this coupled system and the message extraction procedure is illustrated with the help of simulated results.
In this paper, a new scheme is addressed for estimating all unknown parameters of multiple time d... more In this paper, a new scheme is addressed for estimating all unknown parameters of multiple time delayed systems based on nonlinear-observer design. The proposed design scheme is systematic and can be applied to a wide class of multiple time delayed systems. The validity of the proposed nonlinear-observer-based synchronization scheme is confirmed by simulation results.
Projective synchronization of new hyperchaotic Newton–Leipnik system with fully unknown parameter... more Projective synchronization of new hyperchaotic Newton–Leipnik system with fully unknown parameters is investigated in this paper. Based on Lyapunov stability theory, a new adaptive controller with parameter update law is designed to projective synchronize between two hyperchaotic systems asymptotically and globally. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. It is found that the new hyperchaotic system possesses two positive Lyapunov exponents within a wide range of parameters. Numerical simulations on the hyperchaotic Newton–Leipnik system are used to verify the theoretical results.
Journal of Computational and Nonlinear Dynamics, 2007
Detailed bifurcation pattern and stability structure is studied in a modified predator-prey syste... more Detailed bifurcation pattern and stability structure is studied in a modified predator-prey system, with nonmonotonic response function. It is observed that almost all the parameters of the system have a positive influence as far as bifurcation is concerned. The analysis is done with the help of the package MATCONT. In the second stage of the analysis the detailed structure of the normal form is obtained after the corresponding position of Hopf bifurcation and Bogdanov-Takens bifurcation are identified with the help of a modified approach recently proposed by Kuznetsov (1995, 2 where ␣ ജ 0, ␦ Ͼ 0, ജ 0, and  Ͼ −2 ͱ ␣ are parameters of the system. The coefficient "a" represents the intrinsic growth rate of the prey, ␦ is the natural death rate of the predator, and stands then proceeding as in Ref. ͓17͔ we get, a 3 = −1194.389148, b 3 = −1898.968608, and a 4 = 35131.19539, b 4 = −53953.71848, which indicates that a 2 b 4 Ͻ 0, showing that we have a BT bifurcation which is nondegenerate and for which a 2 b 2 0. Therefore, the normal form for nondegenerate codimension 3 BT bifurcation is
The effect of delay feedback control and adaptive synchronization is studied near subcritical Hop... more The effect of delay feedback control and adaptive synchronization is studied near subcritical Hopf bifurcation of a nonlinear dynamical system. Previously, these methods targeted the nonlinear systems near their chaotic regime but it is shown here that they are equally applicable near the branch of unstable solutions. The system is first analyzed from the view point of bifurcation, and the existence of Hopf bifurcation is established through normal form analysis. Hopf bifurcation can be either sub-critical or super-critical, and in the former case, unstable periodic orbits are formed. Our aim is to control them through a delay feedback approach so that the system stabilizes to its nearest stable periodic orbit. At the vicinity of the sub-critical Hopf point, adaptive synchronization is studied and the effect of the coupling parameter and the speed factor is analyzed in detail. Adaptive synchronization is also studied when the system is in the chaotic regime.
In this Letter, we propose a method for generalized and projective synchronization in modulated t... more In this Letter, we propose a method for generalized and projective synchronization in modulated timedelayed systems using nonlinear active control. Sufficient condition for generalized synchronization is calculated analytically by Krasovskii-Lyapunov stability theory. The validity of the proposed algorithm has been confirmed by simulation results. The proposed method helps to find the explicit form of the functional relation between the synchronized variables, for which very few formulations are known at the present moment. Both usual and lag-anticipatory cases can be treated on the same footing.
In this letter we consider a prototype model which is described as an autonomous continuous time ... more In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization phenomenon is examined both numerically and analytically using the Krasovskii-Lyapunov functions. We have applied adaptive coupling law for synchronization,where the coupling equation also contains delay with modulated time. We also studied the effect of cryptography for this coupled system and the message extraction procedure is illustrated with the help of simulated results.
Journal of Physics A-mathematical and Theoretical, 2009
Multiple attractors in a new nonlinear dynamical system recently derived from the derivative nonl... more Multiple attractors in a new nonlinear dynamical system recently derived from the derivative nonlinear Schrodinger (DNLS) equation describing the Alfven turbulence in magnetized plasma are analyzed in the light of geometric characterization of orbit properties, which was originally introduced by Birman and Williams and later systematized by Gilmore, Mindlin, Letellier and others. We observe that the order in which periodic orbits appear is as predicted from their symbolic sequences by the universal sequence. The observed templates of increasing complexity are organized along a spiral (which is actually a two-dimensional homomorphic projection of the original attractor). Examples of explicit templates and their variation with respect to the parameter are exhibited.
Communications in Nonlinear Science and Numerical Simulation, 2008
A detailed investigation is performed about the various zones of stability for delayed Duffing-Va... more A detailed investigation is performed about the various zones of stability for delayed Duffing-Van der Pol system, which in term shows the specific role of delay in the formation of the attractor. Coupling of two such similar systems gives rise to rich dynamics if the coupling also belongs to a delayed class. This gives rise to varieties of synchronization channels -such as anticipatory synchronization and retarded synchronization. As the coefficient of delayed term changes value, it is observed that anticipatory synchronization makes way to phase synchronization. The onset of these various mechanisms are tested by the computation of similarity function and probability of recurrence. In the study of phase synchronization the machinery of empirical mode decomposition (EMD) analysis is adapted and lastly maximal Lyapunov exponent is computed as a verifying criterion.
Communications in Nonlinear Science and Numerical Simulation, 2007
A forced scalar delay dynamical system is analyzed from the perspective of bifurcation and synchr... more A forced scalar delay dynamical system is analyzed from the perspective of bifurcation and synchronization. In general first order differential equations do not exhibit chaos, but introduction of a delay feedback makes the system infinite dimensional and shows chaoticity. In order to study the dynamics of such a system, Galerkin projection technique is used to obtain a finite dimensional set of ordinary differential equations from the delay differential equation. We compare the results of simulation with those obtained from direct numerical simulation of the delay equation to ascertain the accuracy of the truncation process in the Galerkin approximation. We have considered two cases, one with five and the other with eight shape functions. Next we study two types of synchronization by considering coupling of the above derived equations with a forced dynamical system without delay. Our analysis shows that it is possible to have synchronization between two such systems. It has been shown that the chaotic system with delay feedback can drive the system without delay to achieve synchronization and the opposite case is also equally valid. This is confirmed by the evaluation of the conditional Lyapunov exponents of the systems.
The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs)... more The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) described by the one-dimensional quantum Zakharov equations (QZEs) is reinvestigated. A Galerkin type approximation is used to reduce the QZS to a simplified system (SS) of nonlinear ordinary differential equations which governs the temporal behaviors of the slowly varying envelope of the high-frequency electric field and the low frequency density fluctuation. This SS is then shown to establish the coexistence of novel hyperchaotic attractors, whose appearance is explained by means of the analysis of Lyapunov exponent spectra as well as the Kaplan-Yorke dimension. The system has an equilibrium point which depends parametrically on the nondimensional quantum parameter (H) proportional to quantum diffraction, the plasmon number (N) and the wave number of perturbation (α), and which can evolve into periodic, quasi-periodic, chaotic and hyperchaotic states in both semiclassical and quantum cases.
We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical ... more We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series. Sufficient condition for synchronization is derived using Krasovskii-Lyapunov theory. This scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations. One of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available. We present numerical examples for Mackey-Glass system with periodic delay time which are used to illustrate the validity of this scheme. The corresponding numerical results and the effect of external noise are also studied.
The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Base... more The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.
In this article, we have shown that using delay dynamical systems as base, one can use the modula... more In this article, we have shown that using delay dynamical systems as base, one can use the modulation of the various parameters, to transmit multiple signals through a single chaotic time series. It is shown that under certain conditions the original signals and parameters of the driving signals can be recovered with the help of an adaptive demodulator. An important aspect of the present method is that the communication is possible between two time-delayed systems with parameter mismatch using lag and anticipatory synchronization. The whole idea is presented on the basis of Mackey-Glass system, with variable time delay.
In this Letter, dual synchronization in modulated time delay system using delay feedback controll... more In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dualanticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey-Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis.
Communications in Nonlinear Science and Numerical Simulation, 2010
A new type of linear observer based projective, projective anticipating and projective lag synchr... more A new type of linear observer based projective, projective anticipating and projective lag synchronization of time-delayed Rössler system is studied. Along with this, the approach arbitrarily scales a drive system attractor and hence a similar chaotic attractor of any desired scale can be realized with the help of a synchronizing scaling factor. A scalar synchronizing output is considered where the output equation includes both the delay and non-delay terms of the nonlinear function. The condition for synchronization is derived analytically and the values of the coupling parameters are obtained. Analytical results are verified through numerical investigation and the effect of modulated time delay in the method is discussed. An important aspect of this method is that it does not require the computation of conditional Lyapunov exponents for the verification of synchronization.
Nonlinear processes in magnetized plasma are very much important for the proper understanding of ... more Nonlinear processes in magnetized plasma are very much important for the proper understanding of many space and astrophysical events. One of the most important type of study has been done in the domain of Alfven waves. Here we show that a Galerkin type approximation of the DNLS (Derivative Nonlinear Schrödinger) equation describing such wave propagation leads to a new type of nonlinear dynamical systems, very much rich in chaotic properties. Starting with the detailed analysis of fixed points and stability zones we make an in depth study of the unstable periodic orbits, which span the whole attractor. Next the birth of a Hopf bifurcation is identified and normal form, limit cycle analyzed. In the course of our study the detailed structure of the attractor is analyzed. A possibility of internal crisis is also indicated. These results will help in the choice of the plasma parameters for the actual physical situation.
Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is in... more Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is investigated. We propose an adaptive method that can estimate all the parameters of the response system using the driving signal only. In the past few years, various methods have been developed for estimation of multiparameters of a chaotic system but most of them require more than one time series to estimate all the parameters of a chaotic or hyperchaotic system. The proposed method requires only a single chaotic time series to estimate all the parameters. A sufficient condition for synchronization is derived and it is shown that the numerical results well support the analytic calculations. The synchronized system has applications in cryptographic encoding for digital and analog signals, which is shown with an example.
When two different chaotic oscillators are coupled, generalized synchronization can occur. It may... more When two different chaotic oscillators are coupled, generalized synchronization can occur. It may imply a very complicated relation between the states of drive and response systems. We propose a method that can be used to detect and characterize the generalized synchronization in modulated time-delayed systems. Using Krasovskii–Lyapunov theory, sufficient condition for generalized synchronization is derived. The proposed technique has been applied to synchronize prototype and Ikeda models by numerical simulation.
In this letter we consider a prototype model which is described as an autonomous continuous time ... more In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization phenomenon is examined both numerically and analytically using the Krasovskii-Lyapunov functions. We have applied adaptive coupling law for synchronization,where the coupling equation also contains delay with modulated time. We also studied the effect of cryptography for this coupled system and the message extraction procedure is illustrated with the help of simulated results.
In this paper, a new scheme is addressed for estimating all unknown parameters of multiple time d... more In this paper, a new scheme is addressed for estimating all unknown parameters of multiple time delayed systems based on nonlinear-observer design. The proposed design scheme is systematic and can be applied to a wide class of multiple time delayed systems. The validity of the proposed nonlinear-observer-based synchronization scheme is confirmed by simulation results.
Projective synchronization of new hyperchaotic Newton–Leipnik system with fully unknown parameter... more Projective synchronization of new hyperchaotic Newton–Leipnik system with fully unknown parameters is investigated in this paper. Based on Lyapunov stability theory, a new adaptive controller with parameter update law is designed to projective synchronize between two hyperchaotic systems asymptotically and globally. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. It is found that the new hyperchaotic system possesses two positive Lyapunov exponents within a wide range of parameters. Numerical simulations on the hyperchaotic Newton–Leipnik system are used to verify the theoretical results.
Journal of Computational and Nonlinear Dynamics, 2007
Detailed bifurcation pattern and stability structure is studied in a modified predator-prey syste... more Detailed bifurcation pattern and stability structure is studied in a modified predator-prey system, with nonmonotonic response function. It is observed that almost all the parameters of the system have a positive influence as far as bifurcation is concerned. The analysis is done with the help of the package MATCONT. In the second stage of the analysis the detailed structure of the normal form is obtained after the corresponding position of Hopf bifurcation and Bogdanov-Takens bifurcation are identified with the help of a modified approach recently proposed by Kuznetsov (1995, 2 where ␣ ജ 0, ␦ Ͼ 0, ജ 0, and  Ͼ −2 ͱ ␣ are parameters of the system. The coefficient "a" represents the intrinsic growth rate of the prey, ␦ is the natural death rate of the predator, and stands then proceeding as in Ref. ͓17͔ we get, a 3 = −1194.389148, b 3 = −1898.968608, and a 4 = 35131.19539, b 4 = −53953.71848, which indicates that a 2 b 4 Ͻ 0, showing that we have a BT bifurcation which is nondegenerate and for which a 2 b 2 0. Therefore, the normal form for nondegenerate codimension 3 BT bifurcation is
The effect of delay feedback control and adaptive synchronization is studied near subcritical Hop... more The effect of delay feedback control and adaptive synchronization is studied near subcritical Hopf bifurcation of a nonlinear dynamical system. Previously, these methods targeted the nonlinear systems near their chaotic regime but it is shown here that they are equally applicable near the branch of unstable solutions. The system is first analyzed from the view point of bifurcation, and the existence of Hopf bifurcation is established through normal form analysis. Hopf bifurcation can be either sub-critical or super-critical, and in the former case, unstable periodic orbits are formed. Our aim is to control them through a delay feedback approach so that the system stabilizes to its nearest stable periodic orbit. At the vicinity of the sub-critical Hopf point, adaptive synchronization is studied and the effect of the coupling parameter and the speed factor is analyzed in detail. Adaptive synchronization is also studied when the system is in the chaotic regime.
In this Letter, we propose a method for generalized and projective synchronization in modulated t... more In this Letter, we propose a method for generalized and projective synchronization in modulated timedelayed systems using nonlinear active control. Sufficient condition for generalized synchronization is calculated analytically by Krasovskii-Lyapunov stability theory. The validity of the proposed algorithm has been confirmed by simulation results. The proposed method helps to find the explicit form of the functional relation between the synchronized variables, for which very few formulations are known at the present moment. Both usual and lag-anticipatory cases can be treated on the same footing.
In this letter we consider a prototype model which is described as an autonomous continuous time ... more In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization phenomenon is examined both numerically and analytically using the Krasovskii-Lyapunov functions. We have applied adaptive coupling law for synchronization,where the coupling equation also contains delay with modulated time. We also studied the effect of cryptography for this coupled system and the message extraction procedure is illustrated with the help of simulated results.
Journal of Physics A-mathematical and Theoretical, 2009
Multiple attractors in a new nonlinear dynamical system recently derived from the derivative nonl... more Multiple attractors in a new nonlinear dynamical system recently derived from the derivative nonlinear Schrodinger (DNLS) equation describing the Alfven turbulence in magnetized plasma are analyzed in the light of geometric characterization of orbit properties, which was originally introduced by Birman and Williams and later systematized by Gilmore, Mindlin, Letellier and others. We observe that the order in which periodic orbits appear is as predicted from their symbolic sequences by the universal sequence. The observed templates of increasing complexity are organized along a spiral (which is actually a two-dimensional homomorphic projection of the original attractor). Examples of explicit templates and their variation with respect to the parameter are exhibited.
Communications in Nonlinear Science and Numerical Simulation, 2008
A detailed investigation is performed about the various zones of stability for delayed Duffing-Va... more A detailed investigation is performed about the various zones of stability for delayed Duffing-Van der Pol system, which in term shows the specific role of delay in the formation of the attractor. Coupling of two such similar systems gives rise to rich dynamics if the coupling also belongs to a delayed class. This gives rise to varieties of synchronization channels -such as anticipatory synchronization and retarded synchronization. As the coefficient of delayed term changes value, it is observed that anticipatory synchronization makes way to phase synchronization. The onset of these various mechanisms are tested by the computation of similarity function and probability of recurrence. In the study of phase synchronization the machinery of empirical mode decomposition (EMD) analysis is adapted and lastly maximal Lyapunov exponent is computed as a verifying criterion.
Communications in Nonlinear Science and Numerical Simulation, 2007
A forced scalar delay dynamical system is analyzed from the perspective of bifurcation and synchr... more A forced scalar delay dynamical system is analyzed from the perspective of bifurcation and synchronization. In general first order differential equations do not exhibit chaos, but introduction of a delay feedback makes the system infinite dimensional and shows chaoticity. In order to study the dynamics of such a system, Galerkin projection technique is used to obtain a finite dimensional set of ordinary differential equations from the delay differential equation. We compare the results of simulation with those obtained from direct numerical simulation of the delay equation to ascertain the accuracy of the truncation process in the Galerkin approximation. We have considered two cases, one with five and the other with eight shape functions. Next we study two types of synchronization by considering coupling of the above derived equations with a forced dynamical system without delay. Our analysis shows that it is possible to have synchronization between two such systems. It has been shown that the chaotic system with delay feedback can drive the system without delay to achieve synchronization and the opposite case is also equally valid. This is confirmed by the evaluation of the conditional Lyapunov exponents of the systems.
The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs)... more The nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) described by the one-dimensional quantum Zakharov equations (QZEs) is reinvestigated. A Galerkin type approximation is used to reduce the QZS to a simplified system (SS) of nonlinear ordinary differential equations which governs the temporal behaviors of the slowly varying envelope of the high-frequency electric field and the low frequency density fluctuation. This SS is then shown to establish the coexistence of novel hyperchaotic attractors, whose appearance is explained by means of the analysis of Lyapunov exponent spectra as well as the Kaplan-Yorke dimension. The system has an equilibrium point which depends parametrically on the nondimensional quantum parameter (H) proportional to quantum diffraction, the plasmon number (N) and the wave number of perturbation (α), and which can evolve into periodic, quasi-periodic, chaotic and hyperchaotic states in both semiclassical and quantum cases.
We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical ... more We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series. Sufficient condition for synchronization is derived using Krasovskii-Lyapunov theory. This scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations. One of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available. We present numerical examples for Mackey-Glass system with periodic delay time which are used to illustrate the validity of this scheme. The corresponding numerical results and the effect of external noise are also studied.
The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Base... more The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.
In this article, we have shown that using delay dynamical systems as base, one can use the modula... more In this article, we have shown that using delay dynamical systems as base, one can use the modulation of the various parameters, to transmit multiple signals through a single chaotic time series. It is shown that under certain conditions the original signals and parameters of the driving signals can be recovered with the help of an adaptive demodulator. An important aspect of the present method is that the communication is possible between two time-delayed systems with parameter mismatch using lag and anticipatory synchronization. The whole idea is presented on the basis of Mackey-Glass system, with variable time delay.
In this Letter, dual synchronization in modulated time delay system using delay feedback controll... more In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dualanticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey-Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis.
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Papers by Dibakar Ghosh