Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor

Abstract

At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility and local activity, locally active discrete memristors (LADMs) are also suitable for simulating synapses. In this paper, we use a LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

“…In this section, the memristor coupled neuron network governed by system (3) is realized by using off-the-shelf circuit components, as shown in Fig. 20, in which four crucial bipolar transistors MPS2222 and two additional operational amplifiers compose a differential amplifier to realize the hyperbolic tangent function; [50][51][52][53][54][55] the time delay function is realized by the embedded delay module in Multisim software; the operational amplifiers TL082CD and the analog multipliers AD633AN are biased with ±15 V. According to Kirch-038701-10 hoff's laws, the obtained circuit equations can be written as…”

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

“…In recent years, chaotic systems have gradually become a popular issue in nonlinear scientific research due to their complex phenomena in nonlinear systems. [1][2][3][4][5][6][7][8][9][10] In general, a system with one positive Lyapunov exponent (LE) is called a chaotic system and a chaotic system with at least two Lyapunov exponents (LEs) greater than zero is called a hyperchaotic system. [11][12][13] Hyperchaos belongs to a kind of chaos but since hyperchaotic systems have at least two positive LEs, their dynamical behavior folds and expands in more directions, and the dynamic properties of hyperchaotic systems are more complex than those of chaotic systems.…”

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

“…[37][38][39][40][41][42] Therefore, discrete neuron models are more suitable for simulating large-scale neu-ral networks and conducting general research, such as generating chaotic trajectories, pattern recognition, and analyzing synchronized firing behaviors. [43][44][45][46][47][48][49][50][51] As a result, research on discrete neurons has become a hot topic in recent years. In discrete memristor-coupled neural networks, complex dynamical behaviors have been discovered, including coexisting attractors, [52][53][54][55][56] synchronization transitions, and synchronization coexistence.…”