INTERNATIONAL JOURNAL FOR INNOVATIVE RESEARCH IN MULTIDISCIPLINARY FIELD

Abstract:    The predator-prey interaction is one of the most powerful forces shaping an ecosystem. The dynamic relationship between a predator and its prey, particularly when a top predator exists, has profound and cascading impacts on the entire ecosystem. In summary, the health of an ecosystem is often dependent on the presence and stability of its top predator population, as they provide the top-down structure necessary to prevent one species from dominating and to maintain ecological complexity. Recently, the dynamical behaviors of a fractional order three species food chain model with a simplified Holling type IV functional response was studied by S.Mondal by incorporating memory effect (Applied Mathematical Biosystems, 1(1),10-21, 2025). He shown that the fractional order system shows more complex dynamics, like chaos, bifurcation for lower memory as the fractional order becomes larger and shows more simpler dynamics for higher memory as the fractional order decreases. Some qualitative behaviors like existence, uniqueness, non-negativity and boundedness are discussed in a feasible domain except the dissipativeness of the solutions . He also stated the local and global stability criteria of the interior equilibrium point but however, the proof of local stability criterion was left over. This work extends his work and gives the proof of the local stability criterion of the interior equilibrium point. Dissipativeness of the solutions of fractional order system is also proved in a feasible domain. Numerical examples are also provided to substantiate the analytical findings.