Crosstalk phenomena taking place between synapses can influence signal transmission and, in some cases, brain functions. It is thus important to discover the dynamic behaviors of the neural network infected by synaptic crosstalk. To achieve this, in this paper, a new circuit is structured to emulate the Coupled Hyperbolic Memristors, which is then utilized to simulate the synaptic crosstalk of a Hopfield Neural Network (HNN). Thereafter, the HNN’s multi-stability, asymmetry attractors, and anti-monotonicity are observed with various crosstalk strengths. The dynamic behaviors of the HNN are presented using bifurcation diagrams, dynamic maps, and Lyapunov exponent spectrums, considering different levels of crosstalk strengths. Simulation results also reveal that different crosstalk strengths can lead to wide-ranging nonlinear behaviors in the HNN systems.

中文翻译：

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考虑突触串扰的基于双曲型忆阻器的Hopfield神经网络的动态行为

突触之间发生的串扰现象会影响信号传输，在某些情况下还会影响大脑功能。因此，重要的是发现被突触串扰感染的神经网络的动态行为。为此，在本文中，构造了一种新电路来模拟耦合双曲忆阻器，然后将其用于模拟Hopfield神经网络（HNN）的突触串扰。此后，以各种串扰强度观察到HNN的多重稳定性，不对称吸引子和反单调性。考虑了不同水平的串扰强度，使用分叉图，动态图和Lyapunov指数谱来表示HNN的动态行为。