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Generating two simultaneously chaotic attractors with a switching piecewise-linear controller. (English) Zbl 1045.37018
Summary: It has been demonstrated that a piecewise-linear system can generate chaos under suitable conditions. This paper proposes a novel method for simultaneously creating two symmetrical chaotic attractors – an upper-attractor and a lower-attractor – in a 3D linear autonomous system. Basically dynamical behavior of this new chaotic system is further investigated. Especially, the chaos formation mechanism is explored by analyzing the structure of fixed points and the system trajectories.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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