中文摘要：

由压控忆阻替换三维自激振荡系统的线性耦合电阻,实现了一种新型的四维忆阻自激振荡系统.该系统不存在任何平衡点,但可生成周期、准周期、混沌等隐藏吸引子;特别地,当初始条件不同时,系统出现了不同拓扑结构混沌吸引子或准周期极限环与混沌吸引子的共存现象,以及准周期极限环与多种拓扑结构混沌吸引子的多吸引子现象.理论分析、数值仿真和硬件实验的结果一致,表明了所提出的忆阻自激振荡系统有着十分丰富而复杂的隐藏动力学特性.

英文摘要：

The classical attractors,defined as self-excited attractors,such as Lorenz attractor,R？ssler attractor,Chua＇s attractor and many other well-known attractors,are all excited from unstable index-2 saddle-foci,namely,an attractor with an attraction basin corresponds to an unstable equilibrium.A new type of attractors,defined as hidden attractors,was first found and reported in 2011,whose attraction basin does not intersect with small neighborhoods of the equilibria of the system.Due to the existences of hidden attractors,some particular dynamical systems associated with line equilibrium,or no equilibrium,or stable equilibrium have attracted much attention recently.Additionally,by introducing memristors into existing oscillating circuits or substituting nonlinear resistors in classical chaotic circuits with memristors,a variety of memristor based chaotic and hyperchaotic circuits are simply established and has been broadly investigated in recent years.Motivated by these two considerations,in this paper,we present a novel memristive system with no equilibrium,from which an interesting and striking phenomenon of coexistence of the behaviors of hidden multiple attractors and the corresponding multistability is perfectly demonstrated by numerical simulations and experimental measurements.According to a newly proposed circuit realization scheme,a new type of four-dimensional memristive self-oscillated system is easily implemented by directly replacing a linear coupling resistor in an existing three-dimensional self-oscillated system circuit with a voltage-controlled memristor.The proposed system has no equilibrium,but can generate various hidden attractors including periodic limit cycle,quasi-periodic limit cycle,chaotic attractor,and coexisting attractors and so on.Based on bifurcation diagram,Lyapunov exponent spectra,and phase portraits,complex hidden dynamics with respect to a system parameter of the memristive self-oscillated system are studied.Specially,when different initial conditions are used,the system displ