A Memristor-based Lorenz Chaotic Circuit And Its Stabilization Via Variable-time Impulsive Control

Chaos is a kind of common phenomenon widely happening in natural science and humanities,and has caused the consistent attention of scholars both at home and abroad as a special case of nonlinear field.The method using circuit to study the chaotic behavior so far is broad and effective.At the same time,memristor can be used to as a nonlinear component in the chaotic circuit because of its nonlinear properties,and the design of chaotic circuit based on this also gradually has got the attention of researches.At present,the design of chaotic circuit is based on Chua's circuit,adopting different types of memristor model to replace the nonlinear resistance in the Chua's circuit.The main research method is the fixed-time impulsive control when the impulsive control for the memristor-based chaotic circuit is needed.The design of the memristor-based chaotic circuit and its impulsive control can be considered as follows.First of all,we can try to investigate other types of memristor-based chaotic circuit besides the Chua's circuit.What's more,in impulse control scheme,the variable-time impulsive control is also worth investigating and discussing.This paper takes memristor and Lorenz system as the foundation,further studied memristor-based Lorenz chaos circuit and system stability analysis under variable-time impulsive control.The main research content and innovation are as follows:1.Based on quadratic model of memristor,using simple circuit devices,designed the circuit model of the quadratic memristor.And the circuit model is applied to the Lorenz system,realized the memristor-based Lorenz circuits.Based on the circuit,analysis the dynamic behavior including chaos phenomena of the memristor-based Lorenz system.2.In order to realize the control of the memristive Lorenz system,based on the Lyapunov stability theory,using the principle of impulse control,a variable-time impulsive controller is designed.Via B-equivalence conditions and the comparison system method,we can reduce a variable-time impulsive system to a fixed-time impulsive system by the comparison system method.Numerical simulation results show that the variable-time impulsive controller designed before can realize the memristor-based Lorenz system.