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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Consequences of Prey Breaking Away from a Herd and the Intra-Species Competition in Predator and Super Predator Species

Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 389--405 | DOI:10.5890/DNC.2025.06.011

Tridib Kar$^1$, Prabir Panja$^1$, Dipak Kumar Jana$^2$

$^1$ Department of Applied Science, Haldia Institute of Technology, Haldia-721657, W.B., India

$^2$ Principal, Gangarampur College, Gangarampur, Dakshin Dinajpur 733124, West Bengal, India

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Abstract

To better understand how prey, predators, and super predators interact, a mathematical model has been developed. In the absence of a predator, it is thought that prey grows logistically. It is considered that a portion of prey may live outside the herd of prey and the remaining prey may live inside the herd of prey. It is also considered that predators and super predators may compete with one another within their species. Investigations have been done on the non-negativity and boundedness of the proposed model. The stability of the system is tested around each of the potential equilibrium points. Both theoretical and numerical studies of the Hopf bifurcation's existence conditions have been conducted. According to our study, if there is more prey outside the herd, it will be easier to hunt them, which could lead to an unstable ecology because of the increased predation pressure on the prey. It has been found that an increase in prey consumption rates can lead to ecosystem instability due to the herd of prey. It is observed that the increase of the environmental carrying capacity for prey i.e., if prey are living in a large area outside of the herd, then the hunting of prey may become easy for predators and it may make the ecosystem unstable. It is also evident that the ecology may have stabilized as a result of the super predator's increased saturation constant. A major consequence of the increase in predator conversion rates could be to disrupt the stability of the equilibrium of the model. It has been noted that the model might stabilize when intra-species competition rises.

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