Qualitative Analysis of Food-Web Model through Diffusion-Driven Instability

Abstract

Many food webs exist in the ecosystem, and their survival is directly dependent on the growth rate of primary prey; it balances the entire ecosystem. The spatiotemporal dynamics of three species' food webs was proposed and analyzed in this paper, where the intermediate predator's predation term follows Holling Type IV and the top predator's predation term follows Holling Type II. To begin, we examine the system's stability using linear stability analysis. We first obtained an equilibrium solution set and then used a Jacobian method to investigate the system's stability at a biologically feasible equilibrium point. We investigate random movement in species in the presence of diffusion, establish conditions for system stability, and derive the Turing instability condition. Following that, the Turing instability condition for a spatial food web system is calculated. Finally, numerical simulations are used to validate the findings. We discovered several intriguing spatial patterns (spots, strip, and mixed patterns) that help us understand the dynamics of the real-world food web. As a result, the Turing instability analysis used in the complex food web system is especially relevant experimentally because the associated consequences can be researched and applied to a wide range of mathematical, ecological, and biological models.