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Computational Ecology and Software, 2019, 9(1): 19-36
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Article

Crowding effects and depletion mechanisms for population regulation in prey-predator intraspecific competition model

Kumar G. Ranjith¹, Das Kalyan², K. Lakshminarayan³, Reddy B. Ravindra⁴
¹Department of Mathematics, Anurag Group of Institutions, Venkatapur, Hyderabad-500 088, India
²Department of Basic and Applied Sciences, National Institute of Food Technology Entrepreneurship and Management, Kundli, Sonepat, Haryana -131028, India
³Department of Mathematics, Vidya Jyothi Institute of Technology, Moinabad, Hyderabad-500075, India
⁴Department of Mathematics, Jawaharlal Nehru Technological University, Kukatpally, Hyderabad-500085, India

Received 11 October 2018;Accepted 20 November 2018;Published 1 March 2019
IAEES

Abstract
The current investigation centres on the consequences of intra-specific rivalry involving predators in the predator-prey equation. A careful account of the investigation is offered mathematically of the model to offer insights into important outcomes that result from the interplay of deterministic and stochastic process. In particular, the steadiness and bifurcation investigation of this model find mention. Allowance is also made in this model for a stochastic environment impacted by white noise. While for this particular version, the global stability is predicated under conditions bordering on stochasticity close to environmental concerns. Rivalry among the predator population is without a doubt accommodating for a various predator-prey models by keeping population stable at a positive interior equilibrium. Numerical solutions obtained for the models support the assumptions governing the study.

Keywords intraspecific competition;Hopf-bifurcation;stochasticity;Lyapunov function;discrete model;white noise.

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