Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns

Fractional nonlinear systems have been considered in many fields due to their ability to bring memory-dependent properties into various systems. Therefore, using fractional derivatives to model real-world phenomena, such as neuronal dynamics, is of significant importance. This paper presents the fractional memristive Wilson neuron model and studies its dynamics as a single neuron. Furthermore, the collective behavior of neurons is researched when they are locally and diffusively coupled in a ring topology. It is found that the fractional-order neurons are bistable in some values of the fractional order. Additionally, complete synchronization, lag synchronization, phase synchronization, and sine-like synchronization patterns can be observed in the constructed network with different fractional orders.

Automated summary

This paper introduces the significance and application of fractional nonlinear systems, and proposes a neuronal model based on fractional derivatives. The dynamics of individual neurons and the collective behavior of neurons in a ring topology are investigated.