Diseased Prey with Harvesting Predator in Prey-Predator System – An Analytical Study

Madhusudanan,; Gunasekaran, M.; Vijaya, S.

doi:10.9790/5728-096114118

Cited by 2 publications

(1 citation statement)

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“…One of the fundamental structure in population dynamics is prey-predator interactions which has been described firstly by two pioneers Lotka-Volterra [23,33]. In recent times, many researchers have considered effects of harvesting on various types of prey-predator models [2,10,16,24,25,[34][35][36]. Prey-predator harvesting which is applied on predator population as well as prey population have a strong impact on the dynamic evaluation [3,4].…”

Section: Introductionmentioning

confidence: 99%

Stability, Neimark-Sacker bifurcation and chaos control for a prey-predator system with harvesting effect on predator

Gümüş¹,

Fečkan²

2021

MMN

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This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the model and also the existence and the direction of Neimark-Sacker bifurcation are analyzed. We show that the system undergoes Neimark-Sacker bifurcations by using center manifold theorem and bifurcation theory. A state feedback method is applied in order to control the Neimark-Sacker bifurcation. Moreover, numerical simulations are carried out to demonstrate the theoretical results obtained for stability, bifurcation and chaos control strategy.

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