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The Chaotic Behavior for Some Types of Local Bifurcations

Abstract: In this paper, we will investigate the chaotic behavior  for one-dimensional vector field to undergo a saddle node bifurcation, transcritical bifurcation and pitchfork bifurcation, and also, two-dimensional vector fields to undergo a Hopf bifurcation by calculating Lyapunov exponents.

 Keywords: Chaos; Saddle node bifurcation; Transcritical bifurcation; Pitchfork bifurcation; Hopf bifurcation.

REFERENC

[1] I. M. Talb & H. K. Jassim:On the Chaotic Behavior of Local Bifurcation Systems, M.Sc., University of Babylon , 2008.

[2] H. K. Jassim: On Local Fractional and Chaos of a Three-Dimensional Nonlinear System,. Journal of college of Education for Pure Science, Vol.3, No. 2 (2013), pp. 150–158.

[3] M. Cauley, L. Joseph: An Introduction to Nonlinear Dynamical System and Chaos Theory, Physica Scripta, Vol. T20, 1988.

[4] A. M. Lyapunov:  Stability of Motion, Academic Press, New York, 1966.

[5] L. Adrianova: Introduction to Linear Systems of Differential Equations, Translations of Mathematical Monographs, Vol. 146, AMS, Providence, R.I, 1995.

[6] J. D. Meiss: Differential Dynamical System, The Society for Industrial and Applied Mathematics, 2007.

[7] D. Gulick: Encounter with Chaos," McGraw-Hall, Inc., U.S.A., 1992.

[8] S. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos," Springer-Verlag, New York, 2003.

 

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About the Author

Hassan Kamil Jassim

Iftichar Mudhar Talb, and  Hassan Kamil Jassim 

Department of Mathematics, College of Education for pure sciences, University of Babylon, Babylon, Iraq

Department of Mathematics, College of Education for pure sciences, University of Thi-Qar, Nasiriyah, Iraq

 

Corresponding author e-email: hassan.kamil@yahoo.com


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