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突触串扰由相邻突触间神经递质的溢出引起，对神经系统的放电特性及信号传输有着深远影响。利用两个忆阻器模拟生物神经突触，双向耦合Chialvo离散神经元和Rulkov离散神经元，并考虑耦合状态下突触间的串扰行为，构建一类忆阻突触耦合异质离散神经网络。研究分析表明，神经网络不动点的数量及稳定性依赖于突触串扰强度。同时，通过分析分岔图、相图、李雅普诺夫指数谱和时序图等发现，随着突触串扰强度的变化，神经网络表现出不同的共存放电行为。此外，基于神经元放电序列的相位差及同步因子，研究了不同耦合强度及不同系统初始条件和参数情形下，突触串扰强度对神经网络同步行为的影响。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 paper, two memristors are employed to simulate biological neural synapses and bidirectionally couple Chialvo discrete neuron and Rulkov discrete neuron. Thus, a heterogeneous discrete neural network with memristor-synapse coupling is constructed that takes into account the crosstalk behavior between memristor synapses in the coupled state. The analysis demonstrates that the quantity and stability of fixed points within this neural network intimately 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 property manifests in the coexistence of diverse discharge behaviors, which vary significantly with the synaptic crosstalk strength. Intriguingly, the introduction of control parameter to state variable triggers offset boosting and the emergence of infinite stable states within the neural network. Furthermore, we conducted a comprehensive study to explore the influence of synaptic crosstalk strength on the synchronization behavior of the neural network, considering various coupling strengths, initial conditions, and parameters. Our analysis, which was founded on the phase difference and synchronization factor of neuronal discharge sequences, revealed that the neural network maintains phase synchronization despite the variations of the two crosstalk strengths. The insights gained from this paper provide significant support in elucidating the electrophysiological mechanisms underlying biological neural information processing and transmission. 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.
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Keywords:
- Memristor /
- heterogeneous discrete neural network /
- synaptic crosstalk /
- coexisting discharge /
- phase synchronization
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