APPLICATION OF LAGRANGE MULTIPLIER METHOD FOR COMPUTING FOLD BIFURCATION POINT IN A TWO-PREY ONE PREDATOR DYNAMICAL SYSTEM

We propose an application of the classical Lagrange Multiplier method for computing fold bifurcation point of an equilibrium in a one-parameter family of dynamical systems. We have used the fact that an equilibrium of a system, geometrically can be seen as an intersection between nullcline manifolds of the system. Thus, we can view the problem of two collapsing equilibria as a constrained optimization problem, where one of the nullclines acts as the cost function while the other nullclines act as the constraints.