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

Authors

  • A. H.Kamil Department of Mathematics/University of Thi-Qar
  • K. H. Yasir Department of Mathematics/University of Thi-Qar

Keywords:

ODEs, Bifurcation, Singularly perturbed ODEs, Lyapunov Schmidt Re- duction

Abstract

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

     1.PNG                              

the hypothesis                                                 

     2.PNG                              

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).

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Published

2019-04-25

Issue

Vol. 6 No. 4 (2018)

Section

Articles

How to Cite

Bifurcation of Solution in Singularly Perturbed ODEs by Using Lyapunov Schmidt Reduction. (2019). University of Thi-Qar Journal of Science, 6(4), 145-152. http://jsci.utq.edu.iq/index.php/main/article/view/80