Ecological system with fear induced group defence and prey refuge
Shivam Yadav, Jai Prakash Tripathi, Shrichand Bhuria, Satish Kumar, Tiwari, Deepak Tripathi, Vandana Tiwari, Ranjit Kumar Upadhyay, Yun Kang

TL;DR
This paper analyzes a prey-predator model incorporating fear effects, group defense, and prey refuge, revealing how fear influences stability, bifurcations, and spatial patterns in ecological systems.
Contribution
It introduces a novel prey-predator model with fear, group defense, and refuge, providing detailed bifurcation and stability analysis, including spatial pattern formation.
Findings
High fear stabilizes prey-predator dynamics.
Model exhibits subcritical Hopf bifurcation due to fear.
Spatial patterns like spots and stripes depend on fear and refuge levels.
Abstract
In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii) prey refuge. We provide comprehensive mathematical analysis of extinction and persistence scenarios for both prey and predator species. To better explore the dynamics of the system, a thorough investigation of bifurcation analysis has been performed using fear level, prey birth rate, and prey death rate caused by intra-prey competition as bifurcation parameter. All potential occurrences of bi-stability dynamics have also been investigated for some relevant sets of parametric values. Our numerical evaluations show that high levels of fear can stabilize the prey-predator system by ruling out the possibility of periodic solutions. Also, our model Hopf…
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Evolution and Genetic Dynamics · Evolutionary Game Theory and Cooperation
MethodsDiffusion · Network On Network
