Bifurcation analysis for Shil'nikov Chaos Electro-dissolution of Copper.

Jihan Mustafa Mirkhan; Azad Ibrahim Amen

doi:10.21271/ZJPAS.34.4.9

Authors

Jihan Mustafa Mirkhan Department of Mathematics, Faculty of Science, Soran University, Soran, Erbil, Iraq.
Azad Ibrahim Amen 1Department of Mathematics, College of Basic Education, Salahaddin University- Erbil, Iraq. 2Department of Mathematics, Basic Education College, Raparin University-Ranya, Iraq. 3Department of Mathematics, Faculty of Science, Soran University, Soran, Erbil, Iraq.

DOI:

https://doi.org/10.21271/ZJPAS.34.4.9

Keywords:

Local stability, Transcritical bifurcation, Hopf bifurcation, Copper electro-dissolution

Abstract

This paper is devoted to study the local bifurcations and stability of three dimensional systems that representing a Shil'nikov chaos during copper electro-dissolution. The local stability analysis of equilibrium points has been studied. It is shown that transcritical bifurcation can appears in the system. Also, the existence of Hopf bifurcation of the system around the equilibrium points is studied when the parameter passes through the critical value. Normal form theory is used to study bifurcating periodic solutions.

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