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<p>In this work, the formalization of a methodology for discretizing and fractionalizing continuous systems is provided and applied to the Holling type IV predator–prey system to obtain its fractional order discrete-time (FODT) version with the Caputo difference operator. Furthermore, manifold and equilibria bifurcation analysis for the FODT resulting system are performed via the discriminant of the Cardano formula for third-order polynomial equations, where the flip and fold bifurcations are emerged. We formalize the results achieved on the flip and fold bifurcation for the FODT system, followed by numerical simulations to verify the analysis.</p>

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Bifurcation analysis for the discretized-fractionalized Holling type-IV predator–prey system

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Clemente A. Ramos-Fabian,
  • Nohe R. Cazarez-Castro,
  • Jorge A. López-Rentería

摘要

In this work, the formalization of a methodology for discretizing and fractionalizing continuous systems is provided and applied to the Holling type IV predator–prey system to obtain its fractional order discrete-time (FODT) version with the Caputo difference operator. Furthermore, manifold and equilibria bifurcation analysis for the FODT resulting system are performed via the discriminant of the Cardano formula for third-order polynomial equations, where the flip and fold bifurcations are emerged. We formalize the results achieved on the flip and fold bifurcation for the FODT system, followed by numerical simulations to verify the analysis.