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Network Biology, 2022, 12(4): 142-159
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Article

Analysis of chaotic dynamics: A fractional order glycolysis model

Md. Jasim Uddin, S. M. Sohel Rana
Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

Received 12 August 2022;Accepted 15 August 2022;Published online 16 August 2022;Published 1 December 2022
IAEES

Abstract
Glycolysis model has been considered by Caputo fractional derivative. We give the topological classifications of fixed points of this model. Then, we show analytically that under certain parametric conditions fractional order glycolysis model underlies a Neimark-Sacker (NS) bifurcation and Flip bifurctaion. By using central manifold and bifurcation theory, we confirm the existence and direction of both NS and Flip bifurcations. To reinforce our analytical findings, we perform numerical simulations that include bifurcations, phase portraits, periodic orbits, invariant closed cycles, abrupt emergence of chaos and abrupt elimination of chaos. At the end, OGY method is applied to eliminate chaotic trajectories of the system.

Keywords fractional order glycolysis model;Flip and Neimark-Sacker (NS) bifurcations;Maximum Lyapunov Exponents (MLEs);Fractal Dimensions (FDs);chaos control.



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