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Discretization, bifurcation analysis and chaos control for Schnakenberg model

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Abstract

Schnakenberg model is a system showing sustained oscillations for a simple model of glycolysis in which a metabolic process that converts glucose to provide energy for metabolism. Euler approximation is implemented to obtain discrete version of Schnakenberg model. It is proved that discrete-time system via Euler approximation undergoes Neimark–Sacker bifurcation as well as period-doubling bifurcation is also examined at its unique positive steady-state. Keeping in view the dynamical consistency for continuous models, a nonstandard finite difference scheme is proposed for Schnakenberg model. It is proved that continuous system undergoes Hopf bifurcation at its interior equilibrium, whereas discrete-time system via nonstandard finite difference scheme undergoes Neimark–Sacker bifurcation at its interior fixed point. Some chaos and bifurcation control methods are implemented to both discrete-time models. Numerical simulation is provided to strengthen our theoretical discussion.

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Authors and Affiliations

  1. Department of Mathematics, University of Poonch Rawalakot, Rawalakot, Pakistan

    Qamar Din

  2. Abdus Salam School of Mathematical Sciences, GC University Lahore, Lahore, Pakistan

    Kamran Haider

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  1. Qamar Din
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  2. Kamran Haider
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Din, Q., Haider, K. Discretization, bifurcation analysis and chaos control for Schnakenberg model. J Math Chem 58, 1615–1649 (2020). https://doi.org/10.1007/s10910-020-01154-x

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  • DOI: https://doi.org/10.1007/s10910-020-01154-x

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