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Journal of Applied Nonlinear Dynamics 14(3) (2025) 719--743 | DOI:10.5890/JAND.2025.09.014

S. Magudeeswaran$^1$, S. Vinoth$^2$, R. Vadivel$^3$, Nallappan Gunasekaran$^4$

$^1$ Department of Mathematics, Sree Saraswathi Thyagaraja College, Pollachi, 642 107, Tamilnadu, India

$^2$ Center for Nonlinear and Complex Networks, SRM Institute of Science and Technology, Ramapuram, Chennai, 600089, Tamilnadu, India

$^3$ Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket, 83000, Thailand

$^4$ Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou, 535011, P. R. China

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Abstract

In this work, we propose a ratio-dependent intraguild predation model that incorporates fear and gestation delay. Further, the cost of the intraguild predator's fear is thought to decrease the size of the intraguild prey. The interaction between prey and predator takes place in the form ratio-dependence type. This type of functional response offers a valuable perspective by considering the feeding rates based on the relative abundance of both prey and predators. We first determine the conditions under which positive equilibrium points exist, and then we examine the local stability properties of the equilibria. In order to gain insight into the rich dynamics of the proposed non-delayed model, the occurrence of Hopf-bifurcation with respect to the fear parameter near the interior equilibrium point is discussed. Furthermore, we evaluate the local stability and the possibility of a Hopf bifurcation for the delayed model. The direction and stability of the Hopf bifurcation are also studied using the center manifold theorem. Finally, we conduct the numerical simulations to demonstrate our analytical results.

Acknowledgments

The corresponding author would like to thank SRM IST, Ramapuram, India, for their financial support, vide number SRM/IST-RMP/RI/004. Moreover, the authors are very much grateful to the anonymous reviewers and the editor Albert C.J. Luo for their constructive comments and valuable suggestions to improve the quality and presentation of the manuscript significantly.

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