Modeling the fear effect and stability of non-equilibrium patterns in mutually interfering predator–prey systems

• Published in: Applied mathematics and computation 2020-04, Vol.371, p.124948, Article 124948
• Main Authors: Tiwari, Vandana, Tripathi, Jai Prakash, Mishra, Swati, Upadhyay, Ranjit Kumar
• Format: Article
• Language: English
• Subjects: Fear effect; Hopf-bifurcation; Periodic orbits; Predator–prey interactions; Transcritical bifurcation; Turing pattern
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2019.124948

Recent demographic experiments have demonstrated that both birth and survival in free-living animals are essentially affected due to having sufficient exposure to predators and further leaving physiological stress effects. In this paper, we have proposed and analyzed a predator–prey interaction model with Beddington–DeAngelis functional response (BDFR) and incorporating the cost of fear into prey reproduction. Stability analysis and the existence of transcritical bifurcation are studied. For the spatial system, the Hopf-bifurcation around the interior equilibrium, stability of homogeneous steady state, direction and stability of spatially homogeneous periodic orbits have been established. Using Normal form of the steady state bifurcation, the possibility of pitchfork bifurcation has been established. The impact of the level of fear and mutual interference on the stability and Turing patterns of the spatiotemporal system have been discussed in detail. Simulation results ensure that the fear of predator stabilizes the system dynamics and cost the overall population size of the species.