Research On Changing Chaotic Systems’ Characteristics By Linear Augmentation Control

Chaos control,as the most important subject of chaos application research,has always received wide attention.It mainly refers that influencing the dynamic behavior of a chaotic system effectively through a certain control strategy to make it develop into a state,which is actually needed.From the purpose of realization,the research of chaos control is mainly divided into chaos enhancement and chaos suppression.Chaos enhancement mainly refers to the enhancement of the chaotic strength of the nonlinear system to make the signal more disordered.Therefore,the chaotic signal can be used to encrypt images or audio,and chaotic can be widely used in security communication and other fields.Chaos suppression mainly refers to weakening or eliminating the chaotic phenomenon in the system,so that it will not cause damage to some actual projects.So far,a large number of control methods have been proposed,many of which have achieved effective control in their own research fields,but still have extremely high research value in other fields.Linear augmentation control is one of them,which control the nonlinear system by coupling a linear system and changing the coupling strength between the two systems.And study found that this control has unique advantages and flexibility in controlling the equilibrium point of the nonlinear system.In this paper,based on the linear augmentation control method,a series of chaotic systems with different characteristics are taken as the research object,and the change trend of their dynamic characteristics is analyzed and studied.The specific research results are as follows:1)Compositing coexisting attractors by linear augmentation control.Based on three chaotic systems that can produce different types of coexisting attractors,linear augmentation control is introduced.In the process of control,the increase of coupling parameter value will cause the original equilibrium point of the system to move,especially the index-2 saddle-focus equilibrium points,which will affect the original motion trajectory of the system and finally realize the composition of coexisting attractors.In this whole process of control,the number and stability of the system equilibrium points have not changed,which is different from the existed researches about increasing the scroll number of attractors or compositing attractors by expanding the index-2 saddle-focus equilibrium points.In addition,the corresponding control circuit is very easy to design and implement,and the controlled resistance in the circuit has a definite corresponding relationship with the coupling parameter in the system.2)Suppressing chaos by linear augmentation control.On the basis of three chaotic systems with different dimensions and different scroll numbers,the number of attractors’ scroll or wing are gradually reduced,and the control objective of suppressing the chaotic strength of the system is achieved by introducing linear augmentation control.The essence of this control is that the increase of the coupling parameter value which controls the coupling strength will lead to the movement of the equilibrium point,or even the disappearance of some equilibrium points of the controlled chaotic system.In the process controlled,the dynamic behavior changes of multi-scroll chaotic system are analyzed and characterized by corresponding tools,such as coordinate movement curves of the system equilibrium points,bifurcation diagram and so on.In order to verify the circuit implementability of linear augmentation control to achieve attractor degenerating and suppress the chaotic intensity of the system,the control circuit of three-dimensional four-wing system is designed.The analog circuit simulation is carried out,and the actual hardware circuit is built by using bread board and common discrete components.Circuit experimental results also achieved the control goal,which verified the effectiveness of linear augmentation control further.