不连续时滞分数阶忆阻神经网络的非线性动力学分析

Nonlinear dynamic analysis of discontinuous fractional memristive neural networks with time delay

提出一个具有不连续忆导函数的时滞分数阶忆阻神经网络模型,通过数值仿真研究其复杂非线性动力学行为。首先提出了不连续分数阶忆阻神经网络的数学模型;其次,分别将初值、分数阶及开关阶跃作为分岔参数,通过分岔图、相图、庞加莱截面等数值分析手段验证了其典型的动力学行为。研究表明:不同于传统的倍周期分岔通向混沌的道路,该不连续忆阻神经网络通往混沌的道路为阵发混沌。另外,还揭示了不连续的忆导函数和开关阶跃对分数阶忆阻神经网络动力学行为的内在影响机制。

In this paper,a discontinuous fractional-order memristive-based neural network (FMNN) with time delay is presented and the complex nonlinear dynamics is investigated using the numerical simulation. Initially,a mathematical model of discontinuous FMNN is introduced,afterwards taking the initial value,the fractional order or the switching jump as bifurcation parameters,some typical nonlinear dynamical behaviors are verified using bifurcation diagrams,phase portraits,and Poincaré mappings. The results show that different from period-doubling route,the mechanism behind the emergence of chaos for the discontinuous FMNN is the intermittency route to chaos. Besides,the internal influence mechanism of discontinuous memductance function and the switching jump of memristor on the dynamic behaviors of the proposed FMNN also revealed.