Bifurcation of Solution in Singularly Perturbed ODEs by Using Lyapunov Schmidt Reduction

Abstract

This paper aims to study the bifurcation of solution in singularly perturbed ODEs:

                                   

the hypothesis                                                 

                                   

the bifurcation of solution in the ODE system will be studied by effect of the system by using Lyapunov Schmidt reduction. Is the study of behaviour of solution of singularly perturbed ODEs when perturbation parameter  The bifurcation of solution in this kind of ordinary differential equation was studied in n-dimensional. Sufficient conditions for the system to undergoes (fold,transcritical and pitchfork) bifurcation are given. The ODE will be reduced to an equivalent system by using Lyapunov Schmidt reduction method. Moreover, for this purpose of obtaining curve of the system (Fast-Slow system).