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Bifurcation analysis and chaos control in discrete-time glycolysis models. (English) Zbl 1384.92030
Summary: In this paper, the qualitative behavior of two discrete-time glycolysis models is discussed. The discrete-time models are obtained by implementing forward Euler’s scheme and nonstandard finite difference method. The parametric conditions for local asymptotic stability of positive steady-states are investigated. Moreover, we discuss the existence and directions of period-doubling and Neimark-Sacker bifurcations with the help of center manifold theorem and bifurcation theory. OGY feedback control and hybrid control methods are implemented in order to control chaos in discrete-time glycolysis model due to emergence of period-doubling and Neimark-Sacker bifurcations. Numerical simulations are provided to illustrate theoretical discussion.

MSC:
92C40 Biochemistry, molecular biology
37N25 Dynamical systems in biology
34C23 Bifurcation theory for ordinary differential equations
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