Bifurcations and Hyperchaos in Magnetoconvection of Non-Newtonian Fluids

Abstract

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.

Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

“…Recently, Layek and Pati have introduced a four-dimensional mathematical model which describes a hyperchaotic behavior in magnetoconvection of couple-stress fluid system by imposing a vertical magnetic field is studied. This model is given by the following equations [24]:…”

“…In this paper, we propose a observer based synchronization under a master-slave configuration. Such scheme, lie in a fuzzy-based sliding-mode observer (FSMO) design for a hyperchaotic Lorenz-type system reported in Reference [24]. Firstly, the proposed methodology consists in designing a SMO for the hyperchaotic system by means of Lyapunov analysis.…”