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

Abstract

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.

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

“…In recently years, the dynamical behavior of fractional-order neural networks (FONN) was widely studied in [22][23][24][25][26][27][28][29][30], especially fractional-order memristive neural networks (FOMNNs) [31][32][33][34][35][36][37][38][39][40][41]. Chen et al investigated Mittag-Leffler synchronization of a FOMNN by using an M-matrix method and set-valued theory in [31].…”

“…State estimation of delayed FOMNNs with uncertainty were studied in [35][36][37], and some new conclusions were obtained when the activation functions satisfy the different continuous and bound conditions. In [38], a new fractional-order memristive Wilson neuron model with the fractal-fractional derivative was intensively developed. The rich dynamic behaviors with different fractional-orders were proposed, such as complete synchronization, lag synchronization, phase synchronization, and sine-like synchronization, when the neurons are locally and diffusively coupled in a ring topology.…”

Applying exponential unit for breaking symmetry of memristive maps

“…Researchers in this field are now exploring innovative techniques to further improve the scalability and reliability of memristor-based systems, aiming to integrate them into practical computing systems. Additionally, there is ongoing research into utilizing memristors for unconventional applications, such as cognitive computing and brain-inspired architectures, which hold great promise for the future [10][11][12][13]. As memristor technology continues to advance, it is poised to redefine the landscape of memory and computing, offering remarkable advantages that could revolutionize various industries and lead to the development of more efficient and intelligent electronic systems [14][15][16][17].…”