Abstract:
Dynamics of interacting biological species has been studied in the past few decades from various
angles. Many species become extinct and many others are at the verge of extinction due to
several reasons like, over exploitation, over predation, environmental pollution, mismanagement
of natural resources etc. Establishing the conditions for the stability of ecosystems and for stable
coexistence of interacting populations is a problem of the highest priority in mathematical
ecology. Bearing this in mind, in this study the stability of prey predator in the absence of delay
was clearly stated. The minimum cutoff value at which the system loses its stability was also
pointed out. Furthermore, the existence of global stability without linearizing the model was
proved with an appropriate condition. Finally, non-existence of limit cycle at positive
equilibrium was proved by Dulac’s criterion.
