Application of Lagrange Multiplier Method for Computing Fold Bifurcation Point in A Two-Prey One Predator Dynamical System

Marwan Marwan; Johan Matheus Tuwankotta; Eric Harjanto

doi:10.22342/jims.24.2.595.%p

Application of Lagrange Multiplier Method for Computing Fold Bifurcation Point in A Two-Prey One Predator Dynamical System

Marwan Marwan, Johan Matheus Tuwankotta, Eric Harjanto

Abstract

We propose by means of an example of applications of the classical Lagrange Multiplier Method for computing fold bifurcation point of an equilibrium ina 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.

Keywords

Fold Bifurcation, Constrained Extremum, Dynamical Systems

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References

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DOI: https://doi.org/10.22342/jims.24.2.595.%25p