Hidden Attractor And Its Dynamics In Time-delayed Memristor Chaotic System

Memristor is a typical nonlinear electronic component,which has the nonlinear volt-ampere characteristic curve and is different from the known resistor,capacitor and inductor.It can be widely used in the fields of integrated circuits,secure communication,large capacity storage,etc.It is significant to study the nonlinear characteristics of memristor for the design and produce of a memristor device.Recently,hidden attractor has been found in low-dimensional nonlinear system.It is distinct from the self-excited chaotic attractor that originates from the unstable stationery point.It is one of the focus in chaotic dynamic study.Time-delayed system is a kind of infinite dimensional system,which is more complicated than a lowdimensional nonlinear system.It is significant to construct a time-delayed memristor system and study the nonlinear dynamics.In this paper,we mainly focus on hidden attractors in the time-delayed memristor systems.The nonlinear dynamics are studied theoretically and numerically.Circuit experiments are also performed corresponding to the theoretical and numerical results.Firstly,three kinds of time-delayed memristor systems are constructed,including the type I system with both real and complex stationery states,the type II system with infinite number of real stationery states and the type III system without any real stationery state.Secondly,the bifurcation conditions for the type I and II systems are theoretically analyzed with the Lambert W function theory and the time-delayed Hopf theory,respectively.The chaotic solutions are found by alternating the delay time along the bifurcation direction.Starting from random initial conditions,hidden attractors are found numerically in all these types of systems.Under the conditions of fixed initial states and changing delayed time,various bifurcation processes have been found,such as period-doubling bifurcation and quasi-period bifurcation etc.As the delay time being fixed and changing the initial states,both self-excited and hidden attractors are found.There are some co-existence phenomena of period,quasi-period and chaotic states.Finally,we design the analog circuits of the proposed time-delayed memristor systems.Under different conditions(including initial conditions and delay time),the circuits simulation experiments are performed.The experimental results are consistent with theoretical and numerical results.