Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

• Published in: Fractal and fractional Vol. 7; no. 1; p. 82
• Main Authors: Ma, Minglin, Lu, Yaping, Li, Zhijun, Sun, Yichuang, Wang, Chunhua
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2023
• Subjects: Analysis; Behavior; Biological effects; Biomimetics; Equilibrium; locally active discrete memristor; Mathematical models; Memristors; multistability; Neural circuitry; Neural networks; Neurons; Numerical analysis; Parameter identification; Simulation methods; Synapses; Synchronism; synchronization transition
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract7010082

In order to enrich the dynamic behaviors of discrete neuron models and more effectively mimic biological neural networks, this paper proposes a bistable locally active discrete memristor (LADM) model to mimic synapses. We explored the dynamic behaviors of neural networks by introducing the LADM into two identical Rulkov neurons. Based on numerical simulation, the neural network manifested multistability and new firing behaviors under different system parameters and initial values. In addition, the phase synchronization between the neurons was explored. Additionally, it is worth mentioning that the Rulkov neurons showed synchronization transition behavior; that is, anti-phase synchronization changed to in-phase synchronization with the change in the coupling strength. In particular, the anti-phase synchronization of different firing patterns in the neural network was investigated. This can characterize the different firing behaviors of coupled homogeneous neurons in the different functional areas of the brain, which is helpful to understand the formation of functional areas. This paper has a potential research value and lays the foundation for biological neuron experiments and neuron-based engineering applications.