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Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form. (English) Zbl 1245.34054
Summary: A new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the four-wing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order form of the system can also generate a chaotic four-wing attractor.

MSC:
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D45 Attractors of solutions to ordinary differential equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
34C23 Bifurcation theory for ordinary differential equations
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