Bionic modeling and dynamics analysis of heterogeneous brain regions connected by memristive synaptic crosstalk

Abstract

The coupling dynamics between different brain regions has long been a gap in the study of neural dynamics. To overcome this bottleneck, the synaptic crosstalk characterized by coupled memristors is creatively connected to different brain regions characterized by two heterogeneous Hopfield neural networks (HNNs), forming a novel bionic memristive synaptic crosstalk coupled-HNN (MSC-HNN) model for the first time. Rigorous boundedness and stability analyses ensure that coupling dynamics are generated within a bounded region. Utilizing innovative dynamics methods, it is revealed that the plasticity of synaptic crosstalk allows MSC-HNN to exhibit homogeneous dynamics properties globally, and the two internal HNNs preserve heterogeneous bifurcation processes and attractors. Interestingly, when the initial conditions undergo slight variations, the multistability phenomenon is simultaneously represented by the coexisting parameter bifurcation and the local basin of attraction, which enhances the diversity of activities in MSC-HNN. Furthermore, these novel dynamics effects are evaluated and validated through quantitative calculations of complexity measures and spectra. Subsequently, the developed analog and digital circuit implementation paradigms confirm the feasibility and practical value of MSC-HNN.