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Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system. (English) Zbl 1348.34102

Summary: Based on Rabinovich system, a 4D Rabinovich system is generalized to study hidden attractors, multiple limit cycles and boundedness of motion. In the sense of coexisting attractors, the remarkable finding is that the proposed system has hidden hyperchaotic attractors around a unique stable equilibrium. To understand the complex dynamics of the system, some basic properties, such as Lyapunov exponents, and the way of producing hidden hyperchaos are analyzed with numerical simulation. Moreover, it is proved that there exist four small-amplitude limit cycles bifurcating from the unique equilibrium via Hopf bifurcation. Finally, boundedness of motion of the hyperchaotic attractors is rigorously proved.

MSC:

34D45 Attractors of solutions to ordinary differential equations
37G10 Bifurcations of singular points in dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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