Coexisting discharge and synchronization of heterogeneous discrete neural network with crosstalk memristor synapses

Abstract

Synaptic crosstalk, which occurs due to the overflow of neurotransmitters between neighboring synapses, holds a crucial position in shaping the discharge characteristics and signal transmission within nervous systems. In this work, two memristors are employed to simulate biological neural synapses and bidirectionally coupled Chialvo discrete neuron and Rulkov discrete neuron. Thus, a heterogeneous discrete neural network with memristor-synapse coupling is constructed, with the crosstalk behavior between memristor synapses in the coupled state taken into account. The analysis demonstrates that the quantity and stability of fixed points within this neural network greatly depend on the strength of synaptic crosstalk. Additionally, through a thorough investigation of bifurcation diagrams, phase diagrams, Lyapunov exponents, and time sequences, we uncover the multi-stable state property exhibited by the neural network. This characteristic manifests as the coexistence of diverse discharge behaviors, which significantly change with the intensity of synaptic crosstalk. Interestingly, the introduction of control parameter into state variables can lead the bias to increase, and also the infinite stable states to occur in the neural network. Furthermore, we comprehensively study the influence of synaptic crosstalk strength on the synchronization behavior of the neural network, with consideration of various coupling strengths, initial conditions, and parameters. Our analysis, which is based on the phase difference and synchronization factor of neuronal discharge sequences, reveales that the neural network maintains phase synchronization despite the variations of the two crosstalk strengths. The insights gained from this work provide important support for elucidating the electrophysiological mechanisms behind the processing and transmission of biological neural information. Especially, the coexisting discharge phenomenon in the neural network provides an electrophysiological theoretical foundation for the clinical symptoms and diagnosis of the same neurological disease among different individuals or at different stages. And the doctors can predict the progression and prognosis of neurological disease based on the patterns and characteristics of coexisting discharge in patients, enabling them to adopt appropriate intervention measures and monitoring plans. Therefore, the research on coexisting discharge in the neural system contributes to the comprehensive treatment of nervous system disease.