Seonguk Kim, Jung-Tae Park
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.
Submitted March 6, 2026. Published September 28, 2026.
Math Subject Classifications: 34A08, 92D25, 34A12, 34D20, 34C23.
Key Words: Caputo fractional derivative; fractional-order predator-prey model; well-posedness; stability; Hopf bifurcation.
DOI: 10.58997/ejde.2026.75
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Seonguk Kim Division of Natural Science, Applied Science, and Mathematics Defiance College Defiance, OH 43512, USA email: skim@defiance.edu |
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Jung-Tae Park School of Liberal Arts Korea University of Technology and Education Cheonan 31253, Korea email: jungtae.park@koreatech.ac.kr |
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