Design and control of a multi-wing dissipative chaotic system
Considering the dissipative condition, a multi-wing chaotic attractor with a unique perspective is designed, using geometry root locus. By using a nonlinear dissipative term, a new structure is proposed to obtain a dissipative chaotic system with a four-wing attractor. The system properties, namely the phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, Poincare maps and local stability, are investigated by numerical simulations. The phenomenon of multiple attractors is discussed and two double-wing smooth chaotic attractors using two different initial conditions are generated. The nonlinear time-delayed inputs are proposed for chaos control of the new system via bifurcation theory. Based on center manifold and normal form theories, the procedure of determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated.
KeywordsDissipative condition Chaotic attractor Multiple attractors Chaos control
- 27.Tian X, Xu R (2016) Stability and Hopf bifurcation of a delayed CohenGrossberg neural network with diffusion. Math Meth Appl Sci 40:293–305Google Scholar
- 38.Hassard BD, Kazarinoff ND, Wan YH (1981) Theory and applications of Hopf bifurcation. CUP Arch 129–138Google Scholar