• MANSOOR AHMED

We investigate a collection of predator-prey models involving n species, where predator behaviors towards prey and nonlinear interactions within species are considered. We explore the limitations of linear analysis near equilibrium points and propose an expansion of the Routh-Hurwitz criteria into the nonlinear domain using Birkhoff’s normal forms for differential equations. This approach elucidates qualitative features such as the structure of orbits around isolated singularities. By applying this method, we can determine properties like the radius of tori and renormalized frequencies, particularly when eigenvalues of the community matrix exhibit small positive real parts. Additionally, we classify various topological configurations near bifurcation points across a relevant set of control parameters. Examples involving two, three, and four species are examined within the framework of normal forms. We end with recommendations regarding how to link a minor subsystem to a larger community and explore the connections between the graphical isocline method and normal forms. This correlation suggests a pathway to extend the analysis of multi-dimensional systems, particularly in situations where insights from the graphical method are insufficient.

Qualitative Characteristics Of Predator-Prey Communities

"Qualitative Characteristics Of Predator-Prey Communities", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 12, page no.h532-h545, December-2023, Available :http://www.jetir.org/papers/JETIR2312767.pdf

"Qualitative Characteristics Of Predator-Prey Communities", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 12, page no. pph532-h545, December-2023, Available at : http://www.jetir.org/papers/JETIR2312767.pdf