Dynamical Analysis and Synchronization of a New Memristive Chialvo Neuron Model

Chialvo is one of the two-dimensional map-based neural models. In this paper, a memristor is added to this model to consider the electromagnetic induction's effects. The memristor is defined based on a hyperbolic tangent function. The dynamical variations are analyzed by obtaining the bifurcation diagrams and Lyapunov spectra. It is shown that the most effective parameters on the dynamics are the magnetic strength and the injected current. The memristive Chialvo can exhibit different neural behaviors. It is also proven that, like the primary Chialvo model, the memristive version has coexisting attractors; an oscillating state coexists with a fixed point. In addition, to understand how memristive neurons behave in a network, two memristive Chialvo models are coupled with electrochemical synapses. By connecting two neurons and calculating the synchronization error, we can determine the system's synchronizability. It is indicated that the electrical coupling is essential for the occurrence of complete synchronization in the network of memristive Chialvo, and the sole chemical coupling does not lead to synchronization.

Automated summary

In this paper, a memristor is added to the two-dimensional neural model Chialvo to consider the effects of electromagnetic induction. The dynamics of the system are analyzed by obtaining bifurcation diagrams and Lyapunov spectra. The study shows that the magnetic strength and injected current are the most effective parameters on the dynamics. The memristive Chialvo can exhibit different neural behaviors and has coexisting attractors, similar to the primary Chialvo model. Furthermore, it is found that electrical coupling is essential for synchronization in the network of memristive Chialvo, while chemical coupling alone does not lead to synchronization.