Article
MSC:
34D06 34H10 34H20 34C28 34D08 34C23 93C40 37D45,
34H10,
34H20,
93C40 | MR 3085401 | Zbl 1276.34043
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Keywords:
chaotic attractors; stable equilibrium; Shilnikov theorem; Lyapunov exponent; synchronization
chaotic attractors; stable equilibrium; Shilnikov theorem; Lyapunov exponent; synchronization
Summary:
By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis 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 stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between the extended Sprott E system and original Sprott E system. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
References:
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