Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

摘要

Although the control of multistability has already been reported, the one with preselection of the desired attractor is still uncovered in systems with more than two coexisting attractors. This work reports the control of coexisting attractors with preselection of the survived attractors in paradigmatic Chua’s system with smooth cubic nonlinearity. Techniques of linear augmentation combined to system invariant parameters like equilibrium points are used to choose the desired surviving attractors among the coexisting ones. Nonlinear dynamical tools including bifurcation diagrams, standard Lyapunov exponents, phase portraits, and cross section of initial conditions are exploited to reveal the selection scenarios of the survived attractor in the multistability control process of Chua’s system. The main crisis towards annihilation of multistability in Chua’s system when varying the coupling strength is interior crisis and border collision. Theoretical and numerical results obtained are further validated with PSpice analysis.