Papers by Alexander Neiman
Physical Review E
We study the collective dynamics of strongly diffusively coupled excitable elements on small rand... more We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.
AIP Conference Proceedings
The electroreceptors of paddlefish (Polyodon spathula) contain two types of internal oscillators,... more The electroreceptors of paddlefish (Polyodon spathula) contain two types of internal oscillators, including a population of stochastic ≈25 Hz oscillators in the sensory epithelia, and a stochastic 45–65 Hz oscillator in each afferent terminal. The function of the epithelial oscillators is unclear. In other hair cell sensory receptors, oscillations in hair cells have been implicated in frequency tuning, such that
Scientific reports, Jun 21, 2017
We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The pe... more We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. We focus on the spiking statistics of the central node, which fires in response to a noisy input at peripheral nodes. We show that, in the strong coupling regime, relevant to myelinated dendritic trees, the spike train statistics can be predicted from an isolated excitable element with rescaled parameters according to the network topology. Furthermore, we show that by varying the network topology the spike train statistics of the c...
AIP Conference Proceedings, 2000
ABSTRACT
Physical Review E, 2016
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulatio... more We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.
AIP Conference Proceedings, 2002
ABSTRACT A wide class of sensory neurons demonstrates spontaneous oscillatory activity. Moreover,... more ABSTRACT A wide class of sensory neurons demonstrates spontaneous oscillatory activity. Moreover, some thermosensitive neurons, for example, electroreceptors of the paddlefish, dogfish, the warm and cold receptors of rat and cat and the caudal photoreceptor of the crayfish, display complicated bifurcation sequences of the spike train patterns as the control parameter, e. g. the temperature, changes. Recent experiments also revealed the existence of low-dimensional chaotic behavior of some thermoreceptors. We study a rather unusual behavior of a bursting neuron exhibiting an explosion of interspike intervals at a certain temperature value. This phenomenon can be qualitatively demonstrated with electro-physiological experiments with the caudal photoreceptor of the crayfish. Furthermore we investigate a modified Hodgkin-Huxley model to understand the experimentally observed abrupt increase of the interspike intervals. We identify this transition with a homoclinic bifurcation of a saddle-focus equilibrium state which is embedded in the chaotic attractor of the system.
Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, Jul 1, 1997
We apply linear response theory to a parallel ensemble of stochastic resonators. We show that for... more We apply linear response theory to a parallel ensemble of stochastic resonators. We show that for a large number of elements the system can be used to process broadband signals without frequency distortions. Both conventional stochastic resonance and aperiodic stochastic ...
Physical Review E, 2016
We study the emergence and coherence of stochastic oscillations in star networks of excitable ele... more We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral nodes of Ranvier are coupled to a central node by myelinated cable segments is used along with a generic model of networked stochastic active rotators. We show that coherent oscillations can emerge due to stochastic synchronization of peripheral nodes and that the degree of coherence can be maximized by tuning the coupling strength and the size of the network. Analytical results are obtained for the strong coupling regime of the active rotator network. In particular, we show that in the strong coupling regime the network dynamics can be described by an effective single active rotator with rescaled parameters and noise.
Acta Phys Pol B, 2006
ABSTRACT Visual signals converge through the layers of the retinal circuitry from the photorecept... more ABSTRACT Visual signals converge through the layers of the retinal circuitry from the photoreceptor cells to the retinal ganglion cells such that nearby ganglion cells are driven by essentially the same visual stimulus. We use computational modeling to address the question whether the experimentally observed degree of synchrony in nearby ganglion cells is due to the common visual stimulus or whether active network circuitry is necessary.
Aps Meeting Abstracts, Mar 1, 2008
AIP Conference Proceedings, 1997
We study the response of a parallel ensemble of stochastic resonators to external signals. For sm... more We study the response of a parallel ensemble of stochastic resonators to external signals. For small signals linear response theory is used. We show that for a large number of elements this ensemble can be used to process broadband signals without frequency distortions. Nonlinear e ects manifest themselves by the phenomenon of synchronization. Although synchronization is not observed at the output of single elements the mean frequency of the collective response is locked by the input signal. It takes place for a su ciently large number of elements in a wide range of internal noise intensities. We also show that the synchronization is accompanied by a nonmonotonous Shannon entropy of the collective output indicating noise-induced order.
Phys Rep Rev Sect Phys Lett, 2004
We review the behavior of theoretical models of excitable systems driven by Gaussian white noise.... more We review the behavior of theoretical models of excitable systems driven by Gaussian white noise. We focus mainly on those general properties of such systems that are due to noise, and present several applications of our ÿndings in biophysics and lasers.
AIP Conference Proceedings, 2009
AIP Conference Proceedings, 2000
We generalize Chirikov's resonance-overlap criterion for the onset of global chaos in Hamiltonian... more We generalize Chirikov's resonance-overlap criterion for the onset of global chaos in Hamiltonian systems to describe the onset of chaotic attractors in weakly dissipative systems.
AIP Conference Proceedings, 2003
ABSTRACT The electrosensory system of paddlefish contains thousands of electroreceptors, which ar... more ABSTRACT The electrosensory system of paddlefish contains thousands of electroreceptors, which are spontaneously active systems producing stochastic biperiodic spike trains, with a wide range of natural frequencies (mean firing rates). There is no morphological or physiological evidence for coupling between electroreceptors: they can be considered as a parallel array of uncoupled stochastic oscillators. Using broadband noise stimulation, we show that noise induces parabolic bursts in single electroreceptors, revealing a new slow time scale. Noise stimulation also leads to synchronization of the burst onsets in different electroreceptors, even though their intraburst firing rates may differ.
AIP Conference Proceedings, 2003
We propose a model for a walker moving on an asymmetric periodic ratchet potential mediated by no... more We propose a model for a walker moving on an asymmetric periodic ratchet potential mediated by noise. The walker has two feet that make steps in patterns. These are represented as two finite size particles coupled through a double-well potential. The system contains three noise sources: two independent white noises, modeling thermal noise, and exponentially correlated common noise. In the case where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns available for ...
Aps Meeting Abstracts, Mar 1, 2008
ABSTRACT We study the influence of noise on a spike adding transitions within the bursting activi... more ABSTRACT We study the influence of noise on a spike adding transitions within the bursting activity in a Hodgkin-Huxley-type model of the leech heart interneuron. Spike adding in this model occur via homoclinic bifurcation of a saddle periodic orbit. Although narrow chaotic regions are observed near bifurcation transition, overall bursting dynamics is regular and is characterized by a constant number of spikes per burst. Experimental studies, however, show variability of bursting patterns whereby number of spikes per burst varies randomly. Thus, introduction of external synaptic noise is a necessary step to account for variability of burst durations observed experimentally. We show that near every such transition the neuron is highly sensitive to random perturbations that lead to and enhance broadly the regions of chaotic dynamics of the cell. For each spike adding transition there is a critical noise level beyond which the dynamics of the neuron becomes chaotic throughout the entire region of the given transition. Noise-induced chaotic dynamics is characterized in terms of the Lyapunov exponents and the Shannon entropy and reflects variability of firing patterns with various numbers of spikes per burst, traversing wide range of the neuron's parameters
Physical Review E Statistical Nonlinear and Soft Matter Physics, Dec 1, 2008
We study information processing in a peripheral sensory receptor system which possesses spontaneo... more We study information processing in a peripheral sensory receptor system which possesses spontaneous dynamics with two distinct rhythms. Such organization was found in the electrosensory system of paddlefish and is represented by two distinct and unidirectionally coupled oscillators, resulting in biperiodic spontaneous firing patterns of sensory neurons. We use computational modeling to elucidate the functional role of spontaneous oscillations in conveying information from sensory periphery to the brain. We show that biperiodic organization resulting in nonrenewal statistics of background neuronal activity leads to significant improvement in information transfer through the system as compared to an equivalent renewal model.
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Papers by Alexander Neiman