Dynamical Effects of Electromagnetic Flux on Chialvo Neuron Map: Nodal and Network Behaviors

Abstract

We consider the dynamical effects of electromagnetic flux on the discrete Chialvo neuron model. It is shown that the model can exhibit rich dynamical behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, and fingered chaotic attractors. The system enters a chaos regime via period-doubling cascades, reverse period-doubling route, antimonotonicity, and via a closed invariant curve to chaos. The results were confirmed using the techniques of bifurcation diagrams, Lyapunov exponent diagram, phase portraits, basins of attraction, and numerical continuation of bifurcations. Different global bifurcations are also shown to exist via numerical continuation. After understanding a single neuron model, a network of Chialvo neurons is explored. A ring-star network of Chialvo neurons is considered and different dynamical regimes such as synchronous, asynchronous, and chimera states are revealed. Different continuous and piecewise continuous wavy patterns were also found during the simulations for negative coupling strengths.

Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

“…Various other network topologies like lattice network [45][46][47][48], multilayer networks [49] in which there can be spiral waves, antiphase synchronization phenomenon. A discrete version of this system might reveal new dynamical behaviors [29,50] as the bifurcation scenarios for both the continuous and discrete systems are different.…”

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

“…Neurons are the fundamental units of structure and function in the nervous system, and they form neural networks through various types of connections. [1] Neural networks play a crucial role in fields such as signal processing, [2,3] associative memory, [4,5] robot control, [6] and image processing. [7][8][9] As is widely known, a memristor is a device that describes the relationship between charge and flux.…”

An absorbing set for the Chialvo map

“…Since its introduction, the Chialvo model has been subject of growing interest. Many authors were studying various aspects of the model, such as the presence of the so-called comb-shaped chaotic structure [19], different types of bifurcations [9,17], the role of switching mechanism for the dynamics of the model [20], reduction to one-dimensional version [12], stochastic effects of neural activity [2], or dynamical effects of electromagnetic flux on the model [16]. The Chialvo map is also used to define local dynamics of nodes that form a network used to model synchronization of many neurons [10].…”