Papers by EZEQUIEL DEL RIO
A few salient features of dissipative solitons in crystal-like lattices of active units
Chaos, Solitons & Fractals, 2021
Abstract A few salient soliton-like wave evolutionary features of one- and two-dimensional lattic... more Abstract A few salient soliton-like wave evolutionary features of one- and two-dimensional lattices of interacting active units are provided here. In the latter case, particular attention is given to the crystal-like triangular lattice. On the one hand, the units are coupled with nearest neighbors anharmonic forces (Morse potential). On the other hand the units are endowed with the possibility of an input-output energy balance that permits evolution to a steady state and the appearance of metastable states which on occasion can be quite long lasting. The lifetimes of such metastable states depend on the lattice parameter values and the wave front width. Eventually, all metastable states evolve to steady translational modes especially under influence of noise.
Abstract-We proposed the use of a Toda-Rayleigh ring as a central pattern generator (CPG) for con... more Abstract-We proposed the use of a Toda-Rayleigh ring as a central pattern generator (CPG) for controlling hexapodal robots. We show that the ring composed of six Toda-Rayleigh units coupled to the limb actuators reproduces the most common hexapodal gaits. We provide an electrical circuit implementation of the CPG and test our theoretical results obtaining fixed gaits. Then we propose a method of incorporation of the actuator (motor) dynamics in the CPG. With this approach we close the loop CPG -environment -CPG, thus obtaining a decentralized model for the leg control that does not require higher level intervention to the CPG during locomotion in a nonhomogeneous environments. The gaits generated by the novel CPG are not fixed, but adapt to the current robot bahvior.
The Role of Noise in Chaotic Intermittency
World Scientific Series on Nonlinear Science Series B, 2021
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021
For universality in the approach, it is customary to appropriately rescale problems to a single o... more For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible noise level) follows a period-doubling cascade from period one to period two to period four to period eight and, eventually, chaos. However, if the intrinsic noise strength significantly enters the evolution, there appears a parallel sequence of period doublings different from the one found in the previous case.
Regular and Chaotic Dynamics, 2020
Intermittency is a route to chaos when transitions between laminar and chaotic dynamics occur. Th... more Intermittency is a route to chaos when transitions between laminar and chaotic dynamics occur. The main attribute of intermittency is the reinjection mechanism, described by the reinjection probability density (RPD), which maps trajectories of the system from the chaotic region into the laminar one. The main results on chaotic intermittency strongly depend on the RPD. Recently a generalized power law RPD has been observed in a wide class of 1D maps. Noise has an impact on the intermittency phenomena and the generalized RPD introduces a novel scenario because it is affected by the noise. An analytical approach was introduced to estimate the noisy RPD (NRPD). In this work we investigate the noisy RPD in two cases: an experimental continuous system, by means of a Poincaré map associated to it, and a numerical map chosen close to the experimental one. In the experimental map we use the internal noise of the circuit, whereas in the numerical map we introduce the noise in the usual way. We have compared both noisy dynamics and found important differences between them, concerning the propagation of the noise effect from the maximum of the map (where the power law is generated) into the laminar region. To mimic the numerical map by the experiment, we introduced an external noise during a short window of time, obtaining similar results to the ones obtained in the internal natural noise case. We found that our methodology developed to study the noise intermittency can be used to investigate which class of noise is present in continuous systems.
Physica A: Statistical Mechanics and its Applications, 2019
h i g h l i g h t s • The total number of solitons in the chain depends on the noise strength. • ... more h i g h l i g h t s • The total number of solitons in the chain depends on the noise strength. • Modes probability distributions are formed by two mechanisms. • The first mechanism determines the living time of the modes. • The second mechanism governs switching between modes. • Analytical approach and numerical simulations is obtained.
A Form of Active Brownian motor-like on a (nonlinear) Toda lattice
AIP Conference Proceedings, 2005
Results are provided about the evolution of a charged Brownian particle (an “electron”) interacti... more Results are provided about the evolution of a charged Brownian particle (an “electron”) interacting with with particles or “units” placed on a one-dimensional Toda lattice. The thermal bath is a Gaussian white noise obeying Einstein’s fluctuation-dissipation theorem. The electron-lattice interaction is modeled by a Coulomb pseudo-potential. Lattice compressions create soliton excitations (dissipative solitons) that may or may not bind the electron. The electron’s eventual trajectory depends on the (noise) temperature and on the value of the Brownian damping coefficient. It also depends on the landscape displayed by the Coulomb pseudo-potential that allows waves traveling in either direction. Hence the system operates as a drifting ratchet, a kind of active Brownian motor for the transport of particles (or charges) along or against the solitonic motion.
Dissipative Solitons and Metastable States in a Chain of Active Particles
International Journal of Bifurcation and Chaos, 2018
The dynamics of a chain of interacting active particles of Rayleigh-type is studied. Particles ar... more The dynamics of a chain of interacting active particles of Rayleigh-type is studied. Particles are interconnected via Morse potential forces. The steady-state modes (attractors) of the chain with periodic boundary conditions look like cnoidal waves with a uniform distribution of the particles’ density maxima along the chain. However, if the system starts from random initial conditions, a metastable state with nonuniform distribution of density maxima is formed. Characteristics of metastable states, excitation probability of different modes and their lifetimes are studied by numerical simulation.
Reinjection Probability Density for Type-III Intermittency With Noise and Lower Boundary of Reinjection
Journal of Computational and Nonlinear Dynamics, 2017
In this paper, we extend a methodology developed recently to study type-III intermittency conside... more In this paper, we extend a methodology developed recently to study type-III intermittency considering different values of the noise intensity and the lower boundary of reinjection (LBR). We obtain accurate analytic expressions for the reinjection probability density (RPD). The proposed RPD has a piecewise definition depending on the nonlinear behavior, the LBR value, and the noise intensity. The new RPD is a sum of exponential functions with exponent α + 2, where α is the exponent of the noiseless RPD. The theoretical results are verified with the numerical simulations.
New Formulation of the Chaotic Intermittency
New Advances on Chaotic Intermittency and its Applications, 2016
As we have seen in the previous chapters, in the classical theory of intermittency the uniform de... more As we have seen in the previous chapters, in the classical theory of intermittency the uniform density of points reinjected from the chaotic to laminar region is a usual hypothesis. In this chapter we reported on how the reinjection probability density (RPD) can be generalized. Estimation of the universal RPD is based on fitting a linear function to experimental data and it does not require a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets. Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Also an analytical method providing the RPD is explained. It is based on the number of null derivatives of the map at the extreme point. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. The new characteristic exponent is developed, that now is not a single number but is a function depending on the whole map, not on the only the local region. In conclusion, a generalization of the classical intermittency theory is present.
Some Applications of the Chaotic Intermittency
New Advances on Chaotic Intermittency and its Applications, 2016
Intermittency has applications in several topics. Therefore, some phenomena where intermittency i... more Intermittency has applications in several topics. Therefore, some phenomena where intermittency is present are described. Applications in Engineering, Physics, Neuroscience, Medicine, and Economy are introduced.
Classical Theory About Noise Effects in Chaotic Intermittency
New Advances on Chaotic Intermittency and its Applications, 2016
The classical theory of intermittency has been introduced in previous chapters. This chapter is d... more The classical theory of intermittency has been introduced in previous chapters. This chapter is devoted to the additive noise effect. Two classical approaches addressing this problem are the most important ones: Fokker–Plank and renormalization group analysis. In any case, they only consider the noise effect in the local map. The noise effect on the RPD is postponed to Chap. 6
New Formulation of the Noise Effects in Chaotic Intermittency
New Advances on Chaotic Intermittency and its Applications, 2016
This chapter is devoted to the noise effect in intermittency. A method to obtain theoretical expr... more This chapter is devoted to the noise effect in intermittency. A method to obtain theoretical expressions for the noisy reinjection probability density function is developed, which basically consists in extending the M(x) function technique used in Chap. 5 to derive the noiseless reinjection probability density. Moreover, this methodology allows to study the noise effect on the intermittency statistical properties for relatively large noise strengths. We also derive analytical approximations for other statistical variables, such as the probability density of the laminar lengths and the average laminar length. This methodology can describe the statistical properties of the noiseless system using the noisy data. Also, we show that occasionally the presence of noise could not be detected due to the results that behave as they would be corresponding to a noiseless system.
Evaluation of the Intermittency Statistical Properties Using the Perron–Frobenius Operator
New Advances on Chaotic Intermittency and its Applications, 2016
We apply the Perron–Frobenius operator to study type-II intermittency. By means of this operator ... more We apply the Perron–Frobenius operator to study type-II intermittency. By means of this operator we can obtain theoretical expressions for the reinjection probability density function, ϕ(x), and the probability density of the laminar lengths, ψ(l), for several maps with type-II intermittency. To validate these expressions we compare the analytical ϕ(x) and ψ(l) functions with numerical data; we find very good accuracy between theoretical equations and numerical simulations. Also, we carry out comparisons between the new ϕ(x) and ψ(l) functions with those obtained using the M(x) function methodology. Finally, we describe the advantages and difficulties of both methodologies.
The Intermittency Route to Chaos
Handbook of Applications of Chaos Theory, 2016
Experimental behavior of a dissipative Toda-Rayleigh ring
AIP Conference Proceedings, 2002
Using a analog electronic circuit for a Toda-Rayleigh ring we study its oscillatory modes and we ... more Using a analog electronic circuit for a Toda-Rayleigh ring we study its oscillatory modes and we show with a simple and robust method how switching between them occurs.
A Prototype 2N-Legged (insect-like) Robot. A Non-Linear Dynamical System Approach
Cognitive Systems Monographs, 2013
A nonlinear closed lattice or ring is proposed as a central pattern generator (CPG) for controlli... more A nonlinear closed lattice or ring is proposed as a central pattern generator (CPG) for controlling hexapodal robots. We show that the ring composed of six anharmonically interacting units coupled to the limb actuators permits to reproduce typical hexapod gaits. We provide an electronic circuit implementation of the CPG providing the corresponding gaits. Then we propose a method to incorporate the actuator (motor) and leg dynamics in the units of the CPG. With this electro-mechanical device we close the loop CPG—environment—CPG, thus obtaining a decentralized approach for the leg control that does not require higher level CPG intervention during locomotion in a non-smooth hence non flat landscape. The gaits generated by our CPG are not rigid, but adapt to obstacles faced by the robot.
A prototype Helmholtz–Thompson nonlinear oscillator
Review of Scientific Instruments, 1992
A prototype electronic (analog) circuit has been built to mimic a nonlinear oscillator proposed a... more A prototype electronic (analog) circuit has been built to mimic a nonlinear oscillator proposed a century ago by Helmholtz in order to account for combinational tones in the drumskin, and more recently by Thompson to account for ship stability to waves in windy situations and its potential and eventual capsize. Besides a careful discussion of elements and their expected performance, several tests have been used to assess the reliability of the prototype.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
A circular lattice (ring) of N electronic elements with Toda-type exponential interactions and Ra... more A circular lattice (ring) of N electronic elements with Toda-type exponential interactions and Rayleigh-type dissipation is used to illustrate wave formation, propagation, and switching between wave modes. A methodology is provided to help controlling modes, thus allowing it to realize any of (N-1) different wave modes (including soliton-type modes) and the switching between them by means of a single control parameter.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
A detailed theoretical and experimental analysis of the possible oscillatory regimes of the dissi... more A detailed theoretical and experimental analysis of the possible oscillatory regimes of the dissipative Toda-Rayleigh lattice system is provided. It is shown that the system has (N-1) oscillatory modes with different space-time scales and two rotatory modes. Using its analog electronic circuit implementation we also show with a simple and robust method how switching between modes occurs.
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Papers by EZEQUIEL DEL RIO