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Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium. (English) Zbl 1276.34043

Authors’ abstract: By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attactor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors according to detailed numerical as well as theoretical analysis. The analytic results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov’s stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronization between the Sprott E system and the original one. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
34H20 Bifurcation control of ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
93C40 Adaptive control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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