Abstract
A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.
Highlights
The memristor is the fourth fundamental circuit element besides the three primary circuit elements, namely resistor, inductor, and capacitor, presented by Chua in 1971 [1]
Xu et al [28] investigated the behavior of neurons coupled by memristor and found that memristive coupling can lead to enhanced synchronization
In 2020, Zandi et al [21] introduced a one-dimensional neuronal map based on the phase space analysis that can exhibit different neuronal behaviors such as action potential, spiking, bursting, chaotic bursting, and myocardial action potential
Summary
The memristor is the fourth fundamental circuit element besides the three primary circuit elements, namely resistor, inductor, and capacitor, presented by Chua in 1971 [1]. Xu et al [28] investigated the behavior of neurons coupled by memristor and found that memristive coupling can lead to enhanced synchronization. The chimera refers to the state in which oscillators split into coherent and incoherent groups [41] These neuronal collective behaviors have been studied in numerous flowbased [42,43,44], and map-based, neuronal models [45,46,47]. The collective behavior of the network of memristive maps is investigated wherein the neurons are coupled via both electrical and chemical synapses.
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