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Journal of Applied Mathematics and Computation

DOI:http://dx.doi.org/10.26855/jamc.2022.09.008

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Analysis of Bifurcation and chaos to Fractional order Brusselator Model

Md. Jasim Uddin

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.

*Corresponding author: Md. Jasim Uddin

Date: September 21,2022 Hits: 283

Abstract

The Caputo fractional derivative has been considered the Brusselator model. A discretization procedure is initially used to construct caputo fractional differential equations for Brusselator model. We list the topological categories for this model fixed points. Then, we demonstrate analytically that a fractional order Brusselator model underpins a Neimark-Sacker (NS) bifurcation and a Flip-bifurcation under specific parametric conditions. We establish the existence and direction of NS and Flip bifurcations by employing central manifold and bifurcation theory. The dynamical behavior of the fractional order Brusselator model has been determined to be extremely sensitive to the parameter values and the initial conditions. It is investigated how the model's dynamics are affected by step size and fractional- order parameters. We run numerical simulations to support our analytic results, including bifurcations, phase portraits, periodic orbits, invariant closed cycles, rapid emergence of chaos, and abrupt removal of chaos. Finally, a hybrid control method is used to stop the systems chaotic trajectory.

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Analysis of Bifurcation and chaos to Fractional order Brusselator Model

How to cite this paper:  Md. Jasim Uddin. (2022) Analysis of Bifurcation and chaos to Fractional order Brusselator Model. Journal of Applied Mathematics and Computation6(3), 356-369.

DOI: http://dx.doi.org/10.26855/jamc.2022.09.008