On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting

Debaldev Jana, Rachana Pathak and Manju Agarwal

Chaos, Solitons & Fractals, 2016, vol. 83, issue C, 252-273

Abstract: Age-selective harvesting where harvesting of species after a certain age is a scientific strategy with respect to biological and economical point of views. By this method we can overcome the unexpected extinction risk of any harvested population due to random harvesting below its maturation (age, body size or weight). The objective of this paper is to study dynamic behavior of preypredator system with alternative form of time delay in harvesting. Arino et al. [2] have given alternative expression for a delayed logistic equation. Using this expression of time delay, a preypredator system with Holling type III functional response and independent age-selective harvesting is proposed and analyzed. We find out the critical values of delay parameters under different dynamical situations and observe that system is stable and unstable when the delay parameters are bellow and above the critical values respectively and there is Hopf bifurcation when delay parameters cross the critical values. System shows these interesting dynamical features under different critical parametric restrictions. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations illustrate the analytical results.

Keywords: Generalist predator; Age-selective harvesting; Direction and stability of Hopf-bifurcation; Normal form theorem (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:83:y:2016:i:c:p:252-273

DOI: 10.1016/j.chaos.2015.12.008

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