ISSN : 2663-2187

Kernel Dynamics in Three Species Ecological Model with Distributed time delay

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Papa Rao AV* and N V S R C Murty Gamini
» doi: 10.33472/AFJBS.6.5.2024. 6438-6449

Abstract

To understand the influence of the delay kernel weight on the dynamics of the three species model with prey, predator and competitor. Here competitor is competing with both the prey and predator species. A distributed time lag is induced in prey predator interaction. The Mathematical model is characterized by the system of integro differential equations. We proved that the solutions are positive and bounded in . The equilibrium point for co-existing state is identified. The local stability analysis is address at this point and shown that the system is asymptotically stable. Global dynamics is addressed by the constructing suitable Lyapunov’s function. The influence of kernel weight is studied using numerical simulation. The exponential kernel is taken for investigation. The kernel weights are significant in system dynamics. We identify the range of kernel strengths which exhibits the Hopf bifurcation nature. The parameters are identified using numerical simulation where the system admits change over behaviour from stable to unstable nature.

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