基于新忆阻器的异质神经元混沌系统的动力学行为分析及电路实现

Dynamical behaviour analysis and circuit implementation of a heterogeneous neuronal chaotic system based on a novel memristor

不同神经元的活动具有较大差异,忆阻电磁感应效应在同质神经元中得到了广泛研究,但鲜有在异质神经元中的研究。首先,基于柯西分布函数与双曲正切函数,提出一种新理想型磁控忆阻器,并对该忆阻器进行电路实现。将新理想型磁控忆阻器引入二维Hindmarsh-Rose(HR)神经元与二维Fitz Hugh-Nagumo(FHN)神经元中,构建具有忆阻电磁感应效应的五维忆阻耦合异质神经元混沌系统。其次,分析该混沌系统的动力学行为,包括相图、庞加莱截面、分岔图、李雅普诺夫指数等。最后,利用Multisim设计该混沌系统吸引子的电路实现,从而验证数值仿真的正确性。结果表明,五维忆阻耦合异质神经元混沌系统能够表现出切分岔、周期、混沌等丰富的非线性动力学行为。

The activities of different neurons are quite different.The memristive electromagnetic induction effect has been widely studied in homogeneous neurons,but there is a lack of research of it in heterogeneous neurons.In in this study,firstly,based on Cauchy distribution function and hyperbolic tangent function,a new ideal flux-controlled memristor is proposed,and its circuit implementation is realized.The new ideal flux-controlled memristor is introduced into a two-dimensional HindmarshRose(HR) neuron and a two-dimensional FitzHugh-Nagumo(FHN) neuron to construct a five-dimensional memristor-coupled heterogeneous neuron chaotic system with memristive electromagnetic induction effect.Secondly,the dynamic behaviors of the chaotic system are analyzed,including phase diagram,Poincaré map,bifurcation diagram,Lyapunov exponents.Finally,the circuit implementation of the chaotic attractors of the chaotic system are designed with Multisim to verify the correctness of the numerical simulation.The results show that the five-dimensional memristor-coupled heterogeneous neuron chaotic system can exhibit rich nonlinear dynamic behaviors such as tangent bifurcation,period and chaos.