Complex dynamics analysis and feedback control for a memristive switched chaotic system

Abstract

Abstract To enrich the chaos theory and improve the complex characteristics of the system. A switched chaotic system is proposed by connecting the memristor to the Rössler system through a time-switching function in this paper. Under the action of the switching function, the system can switch between two subsystems with different structures. The switched system has multiple coexisting attractors for different initial values and exhibits chaotic and quasi-periodic offset boosting, as well as different transient transition behaviors. It is interesting to note that besides the initial-dependent offset boosting, there are three other types of offset boosting behaviors, of which the time-based switching function, combined constant, and switching function offset boosting have not been found in other systems. Since time-based offset boosting does not require the introduction of system variables, it can reduce system design complexity and circuit cost. The novel offset boosting provides a new method for realizing offset boosting behaviors and multi-attractors in chaotic systems. In addition, the switching function can make the attractor self-replicate and produce intermittent chaos, and transient transition behavior also occurs in a short time during the intermittent process. These findings indicate that the switched system has more complex dynamics than either of the two subsystems. Both analog and DSP digital circuits confirm the physical feasibility of the novel offset-boosting behavior. Finally, a feedback controller was designed to further implement the switched system in engineering applications. Theoretical analysis, Matlab numerical calculations, and Multisim circuit simulation show that the state variables of each subsystem can be well controlled under the action of the feedback controller.