Computation of Cusp Bifurcation Point in a Two-Prey One Predator Model using Lagrange Multiplier Method

In this paper we introduce a new method for computing cusp bifurcation point in a system of two prey one predator dynamical system. The method consists of rewriting the system of equations for the equilibria in a constrained optimization problem at where the classical Lagrange Multiplier Method can be applied to derive the fold bifurcation point. By having one extra parameter as free parameter we construct two fold curves which intersect each other nontransversally in a cusp bifurcation point. This result is verified by looking at three section in two-dimensional parameter space by taking one of the parameter constant and study the stability of the equilibria.