Related papers: Periodic and chaotic dynamics in a map-based neuro…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the…
We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K, K{\alpha},…
We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are considered. We discuss bifurcation scenarios explaining the birth of these oscillations and their transformation into tonic spikes. Specific features…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
Understanding of the onset and generic mechanisms of transitions between distinct patterns of activity in realistic models of individual neurons and neural networks presents a fundamental challenge for the theory of applied dynamical…
Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice.…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
We explore the chaotic dynamics and complexity of a neuro-system with respect to variable synaptic weights in both noise free and noisy conditions. The chaotic dynamics of the system is investigated by bifurcation analysis and 0-1 test. A…
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…
Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information…