Well-posedness, stability, and bifurcation of a fractional-order predator-prey model with fear and predator…

Abstract

We study a fractional-order predator-prey model with fear in predator interference and a non-monotonic functional response, formulated via the Caputo derivative. The fractional-order setting incorporates memory effects in the population dynamics and extends the corresponding integer-order system. We first prove well-posedness by establishing the existence and uniqueness of solutions, together with positivity and boundedness. We then analyze the equilibria and derive conditions for local stability in terms of the Jacobian matrix and the fractional order. Sufficient criteria for global asymptotic stability are obtained by using an appropriate Lyapunov function. In addition, we show that the system can undergo a Hopf bifurcation about an interior equilibrium as the fractional order varies. Numerical simulations are provided to illustrate the theoretical results on stability and bifurcation.

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BibTeX RIS

BibTeX

@article{kim2026wellposedness,
  title = {{Well-posedness, stability, and bifurcation of a fractional-order predator-prey model with fear and predator interference}},
  author = {Seonguk Kim and Jung-Tae Park},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = sep,
  url = {http://ejde.math.txstate.edu/Volumes/2026/75/abstr.html},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Well-posedness, stability, and bifurcation of a fractional-order predator-prey model with fear and predator interference
AU  - Seonguk Kim
AU  - Jung-Tae Park
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/75/abstr.html
AB  - We study a fractional-order predator-prey model with fear in predator interference and a non-monotonic functional response, formulated via the Caputo derivative. The fractional-order setting incorporates memory effects in the population dynamics and extends the corresponding integer-order system. We first prove well-posedness by establishing the existence and uniqueness of solutions, together with positivity and boundedness. We then analyze the equilibria and derive conditions for local stability in terms of the Jacobian matrix and the fractional order. Sufficient criteria for global asymptotic stability are obtained by using an appropriate Lyapunov function. In addition, we show that the system can undergo a Hopf bifurcation about an interior equilibrium as the fractional order varies. Numerical simulations are provided to illustrate the theoretical results on stability and bifurcation.
SN  - 1072-6691
ER  -

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