Research articles
ScienceAsia 51 (2026): 1-11 |doi:
10.2306/scienceasia1513-1874.2026.095
Dynamics of a fractional order delayed predator-prey system
with ratio-dependence
Xiao Tanga,b, Ahmadjan Muhammadhajia,b,*
ABSTRACT: In this study, we investigate the dynamical behavior of a fractional-order delayed predator-prey system
with Holling-II type functional response modeled by fractional-order delay differential equations. Initially, the Laplace
transform technique is employed to establish the boundedness of solutions in the absence of time delay. The existence
of solutions is then rigorously established using the zero-point existence theorem, followed by an analysis of the local
stability properties of equilibrium points. By treating the time delay as a bifurcation parameter, we derive explicit
conditions for the occurrence of Hopf bifurcation, demonstrating that the system loses stability and generates a family
of periodic oscillations as the delay parameter crosses critical threshold values. Finally, numerical simulations are
conducted to validate the theoretical results: specific parameter configurations are selected, and different fractional
orders alongside varying delay magnitudes are systematically explored to corroborate the analytical findings.
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| a |
College of Mathematics and System Sciences, Xinjiang University, Urumqi 83, China |
| b |
The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University,
Urumqi 83, China |
* Corresponding author, E-mail: ahmatjanam@aliyun.com
Received 12 May 2025, Accepted 14 Oct 2025
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