Numerical simulation of interacting fish populations with bifurcation

Abstract

This paper presents a numerical simulation of the complex interactions between two competing fish populations with bifurcation. Our first result shows that the co-existence steady-state solution will be stable when the birth rate of each fish population outweighs its death rate. Our second result shows that the stability of the co-existence steady-state solution of the interacting fish populations is lost when the birth and death rates are not changing. Our third result shows that the co-existence steady-state solution will be unstable when the death rate of the fish populations outweighs its birth rate. It is our expectation that these results will provide short-term and a relatively long-term insights in marine ecology.