This paper investigates the Fractional-Order Selkov-Schnakenberg Reaction-Diffusion (FOSSRD) model, a mathematical framework for studying spatiotemporal dynamics, including pattern formation and stability, in chemical and biological systems. The model integrates fractional calculus to capture memory and hereditary effects inherent in complex systems. A comprehensive analysis is conducted, covering local asymptotic stability (LAS) of equilibrium points (EPs) and the impact of key parameters, such as diffusion coefficients and fractional orders (FOs), on dynamic behavior. Semi-analytical solutions and numerical simulations validate the theoretical findings, illustrating the system’s ability to generate diverse spatial patterns and oscillatory dynamics. Applications of the model span biochemical oscillations, cellular signaling pathways, and ecological interactions. The results provide deeper insights into the intricate mechanisms governing nonlinear systems and establish a foundation for further research in higher-dimensional and stochastic extensions of the model.

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The Fractional-Order Selkov-Schnakenberg Reaction-Diffusion Model: Stability and Numerical Simulations

  • Iqbal H. Jebril,
  • Issam Bendib,
  • Adel Ouannas,
  • Salah Boulaaras,
  • Iqbal M. Batiha,
  • Shaher Momani

摘要

This paper investigates the Fractional-Order Selkov-Schnakenberg Reaction-Diffusion (FOSSRD) model, a mathematical framework for studying spatiotemporal dynamics, including pattern formation and stability, in chemical and biological systems. The model integrates fractional calculus to capture memory and hereditary effects inherent in complex systems. A comprehensive analysis is conducted, covering local asymptotic stability (LAS) of equilibrium points (EPs) and the impact of key parameters, such as diffusion coefficients and fractional orders (FOs), on dynamic behavior. Semi-analytical solutions and numerical simulations validate the theoretical findings, illustrating the system’s ability to generate diverse spatial patterns and oscillatory dynamics. Applications of the model span biochemical oscillations, cellular signaling pathways, and ecological interactions. The results provide deeper insights into the intricate mechanisms governing nonlinear systems and establish a foundation for further research in higher-dimensional and stochastic extensions of the model.