Message Signal Encryption Based on Qi Hyper-Chaos System

In this paper, we present a novel 4-dimensional (4D) smooth quadratic autonomous hyperchaotic system with complex dynamics. In order to investigate the dynamics evolution of the system, the Lyapunov exponent spectrum, bifurcation diagram and various phase portraits are provided. The local dynamics of this hyperchaotic system, such as the stability, pitchfork bifurcation, and Hopf bifurcation of equilibrium point, are analyzed by using the center manifold theorem and bifurcation theory. About the global dynamics, the ultimate bound sets of the system are found by combining the Lyapunov function method and appropriate optimization method. Numerical simulations are given to demonstrate the emergence of the two bifurcations and show the ultimate boundary regions.

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Bifurcations and Hyperchaos in Magnetoconvection of Non-Newtonian Fluids

Layek

Pati

2018

Int. J. Bifurcation Chaos

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We report the existence of multiple bifurcations, period-doubling route to chaos and hyperchaos in magnetoconvection of a shallow, electrically conducting non-Newtonian couple-stress fluid layer heated from underneath with vertically imposed magnetic field. By adopting low-order approximations, a four-dimensional dissipative hyperchaotic system with six control parameters is obtained. Both fluid couple-stress and magnetic parameters delay the onset of convection. In contrast to plain couple-stress convection, the magnetic field instigates the occurrence of Andronov–Hopf, Bogdanov–Takens bifurcations with double-homoclinic connection at the origin near the onset of magnetoconvection when the magnetic diffusivity ratio (the ratio of fluid Prandtl number to magnetic Prandtl number) is less than one. Thereafter the system exhibits periodic attractors near subcritical Hopf bifurcation at nonzero equilibrium points undergoing chaos through period-doubling process. Owing to the interaction between the magnetic field and fluid couple-stress, the present model system exhibits hyperchaos via a suddenly created instability during stable oscillation for critical values of the parameters.

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Message Signal Encryption Based on Qi Hyper-Chaos System

Cited by 3 publications

References 11 publications

Two-level chaotic system versus non-autonomous modulation in the context of chaotic voice encryption

Two-level chaotic system versus non-autonomous modulation in the context of chaotic voice encryption

Local Bifurcation Analysis and Global Dynamics Estimation of a Novel 4-Dimensional Hyperchaotic System

Bifurcations and Hyperchaos in Magnetoconvection of Non-Newtonian Fluids

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