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 analysis . Two-dimensional systems have a vast and important dynamics with enormous applications and we study now to explore some of them in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arrowsmith, D.K., Place, L.M.: Dynamical Systems: Differential equations, Maps, and Chaotic Behaviour. Chapman and Hall/CRC (1992)
Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Springer, New York (2001)
Andronov, A.A., Leontovitch, E.A., Gordon, I.I., Maier, A.G.: Qualitative Theory of Second-Order Dynamical Systems. Willey, New York (1973)
Strogatz, S.H.: Nonlinear Dynamics and Chaos with Application to Physics, Biology, Chemistry and Engineering. Perseus Books, L.L.C, Massachusetts (1994)
Jordan, D.W., Smith, P.: Non-linear Ordinary Differential Equations. Oxford University Press (2007)
Lakshmanan, M., Rajasekar, S.: Nonlinear Dynamics: Integrability. Springer, Chaos and Patterns (2003)
Irwin, M.C.: Smooth Dynamical Systems. World Scientific (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer India
About this chapter
Cite this chapter
Layek, G.C. (2015). Phase Plane Analysis. In: An Introduction to Dynamical Systems and Chaos. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2556-0_3
Download citation
DOI: https://doi.org/10.1007/978-81-322-2556-0_3
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2555-3
Online ISBN: 978-81-322-2556-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)