Stability and Boundedness Analysis of a Prey-Predator System with Predator Cannibalism

Stability and Boundedness Analysis...

Abstract

The prey-predator system with predator cannibalism is considered in this
papper. We employ the Lyapunov’s direct method for the prey-predator system
and demonstrate its efficacy. This method is built upon theoretical Lyapunov’s
function that is constructed such that the scalar function and its derivative is
positive and negative definite respectively to determine the dynamic behaviour
of the system considered including stability and boundedness. The results show
that the density functions describing the prey-predator system is better rapidly
converging under certain sufficient conditions obtained by the Lyapunov functional.
We give numeric example to support our findings.