Dynamic Properties and Numerical Simulations of the Fractional Hastings–Powell Model with the Grünwald–Letnikov Differential Derivative

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Abstract
This paper focuses on the dynamical behavior of the fractional-order Hastings–Powell (HP) model. First, a high-precision numerical method is given and the limitations of the method are analyzed. Then, the stability of the equilibrium point of the model is analyzed, numerical simulations of the model with different orders and initial values are carried out, and a comparison is made between the high-precision numerical method and other methods. Finally, the Turing instability analysis and the weak nonlinear analysis of the HP model with diffusion terms are carried out and numerical simulations are performed in a nine-point difference format. The consistency between the numerical results and the numerical simulations is also verified.
Funding Information
  • Inner Mongolia University of Technology (DC2300001252, DC2400003130)
  • the Natural Science Foundation of Inner Mongolia (2024LHMS06025)

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