Abstract
The switching of behavior, from the hyperchaotic to controlled magnetoconvection model, is studied by a feedback control technique. The magnetoconvection model shows hyperchaotic oscillations for different values of parameters: Rayleigh number r, Chandrasekhar number Q, and diffusivity ratio l. Chaotic responses of the magnetoconvection model are considered through boundedness and Lyapunov exponents to specify the place where the controller needs to be applied. The controller for the magnetoconvection model is calculated by using the concept of the Lie derivative, which is the most significant facet of control analytical techniques. Speed and dislocated feedback techniques are also utilized with the consideration of stability analysis through feedback gains. To show the advantages of the feedback control technique, we give a comparison with other control techniques such as speed and dislocated feedback techniques. Simulation results indicate that the analytical strategy for controlling the oscillation is effective and controlled within a small duration of time.
Highlights
MotivationIt was a great breakthrough discovery that irregular motion with strong oscillatory behavior is termed chaotic
These control strategies effectively control the chaos, but according to the comparison, one can see that the state space linearization feedback controls the trajectories efficiently and more effectively as compared to the other two control strategies
According to the accuracy point of view, state space linearization is recommended as it is an analytical technique, whereas with some series of steps, we can design an exact form of controller that controls the system to the required goals
Summary
It was a great breakthrough discovery that irregular motion with strong oscillatory behavior is termed chaotic. Chaotic models have been controlled by the implementation of control techniques for some beneficial purposes. Scitation.org/journal/adv considered, which has a significant effect on the fluid flow In this phenomenon, magnetic field, induced current, and electromagnetic interactions are considered, which have a strong effect on the motion of a fluid.. Layek and Pati constructed a 5D nonlinear system in convection with heat flux in non-Fourier form and established interesting dynamics. Those models related to the above-described phenomenon have vast applications in polymer flows, lubrication systems, medical sciences, the dynamo theory, and many others.
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