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| Dynamical Analysis in a Discrete Fractional Order Harvested Predator-Prey Model Incorporating Fear Effect and Refuge |
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| KeyWord:Dynamical analysis, predator-prey model, harvesting, fear effect, refuge, discrete fractional order |
| Author Name | Affiliation | | Siti Nurul Afiyah | Doctoral Program of Mathematics and Natural Science, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia
Department of Computer Science, Institut Teknologi dan Bisnis Asia, Malang 65113, Indonesia | | Fatmawati | Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia | | Windarto | Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia |
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| Abstract: |
| This paper examines the dynamics of a discrete fractional-order predator-prey model, incorporating the effects of fear, prey refuge, and population harvesting. The fractional-order framework, which accounts for memory-dependent processes, provides a more accurate depiction of biological interactions than traditional integer-order models. Fear is modeled as a factor that reduces predator-prey encounters, while prey refuge offers a sanctuary, altering population dynamics. The inclusion of harvesting further complicates prey population regulation. We identify the system's equilibrium points and conduct a local stability analysis, focusing on the conditions that lead to stability, instability, and bifurcation. Specifically, we examine the Neimark-Sacker bifurcation, where a stable fixed point evolves into a closed periodic orbit. Numerical simulations corroborate the analytical findings, illustrating the pivotal roles that fear, refuge, and harvesting play in shaping system stability and long-term behavior. |
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