Abstract
This paper introduces a hyperchaotic system from the Lü system with a sinusoïdal perturbation. This hyperchaotic system has more complex dynamical behaviors, and can generate 2-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits.
Highlights
Much attention has been paid to the investigation of the existence and applications of hyperchaos
This paper introduces a hyperchaotic system from the Lü system with a sinusoïdal perturbation
Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits
Summary
Much attention has been paid to the investigation of the existence and applications of hyperchaos. It is well known that hyperchaos can only appear in four- or more dimensional systems and is usually generated from a known low-dimensional system [1]-[8] via some control schemes. Some hyperchaotic systems have been discovered as in [9]-[16]. We will report a new hyperchaotic system constructed from the Lü system [17] via a sinusoidal perturbation. The Lü system found in 2004 [17] has many interesting properties such as the existence of two-scroll chaotic attractors with only three equilibria and two 2-scroll chaotic attractors with five equilibria. It is perhaps expected that the Lü system with a sinusoidal perturbation will exhibit more complex dynamical behaviors
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