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Phase Plane Analysis

In: An Introduction to Dynamical Systems and Chaos

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  • G. C. Layek

    (The University of Burdwan, Department of Mathematics)

Abstract

We have so far discussed one-dimensional systems and solution methods for linear systems. As we know analytical solutions of nonlinear systems are very difficult to obtain except for some special nonlinear equations. The essence of this chapter is to give on finding the local solution behaviors of nonlinear systems, known as local analysis. We shall emphasize on qualitative properties of linear and nonlinear systems rather than quantitative analysis or closed-form solution of a system. The qualitative analysis for two-dimensional system is known as phase plane analysisPhase plane analysis . Two-dimensional systems have a vast and important dynamicsDynamics with enormous applications and we study now to explore some of them in this chapter.

Suggested Citation

  • G. C. Layek, 2015. "Phase Plane Analysis," Springer Books, in: An Introduction to Dynamical Systems and Chaos, chapter 0, pages 83-127, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-2556-0_3
    DOI: 10.1007/978-81-322-2556-0_3
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