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2019 | OriginalPaper | Chapter

1. Stability of Equilibriums

Author : Albert C. J. Luo

Published in: Bifurcation and Stability in Nonlinear Dynamical Systems

Publisher: Springer International Publishing

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Abstract

In this chapter, basic concepts of nonlinear dynamical systems are introduced. A local theory of equilibrium stability for nonlinear dynamical systems is discussed. The spiral stability of equilibriums in nonlinear dynamical systems is presented through the Fourier series base. The higher order singularity and stability for nonlinear systems on the specific eigenvectors are developed. The Lyapunov function stability is briefly discussed, and the extended Lyapunov theory for equilibrium stability is also presented.

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next chapter Bifurcations of Equilibrium
Literature
Carr, J.,1981, Applications of Center Manifold Theory, Applied Mathematical Science 35, Springer-Verlag, New York.CrossRef
Coddington, E.A. and Levinson, N., 1955, Theory of Ordinary Differential Equations, New York: McGraw-Hill.MATH
Hartman, P., Ordinary Differential Equations, Wiley, New York. (2nd ed. Birkhauser, Boston Basel Stuttgart, 1964).
Hirsch, M.W., Smale, S. and Devaney, R.L., 2004, Differential Equations, Dynamical Systems, and An Introduction to Chaos, Amsterdam: Elsevier.MATH
Luo, A.C.J., 2008a, A theory for flow switchability in discontinuous dynamical systems, Nonlinear Analysis: Hybrid Systems, 2(4), pp. 1030–1061.MathSciNetMATH
Luo, A.C.J., 2008b, Global Transversality, Resonance and Chaotic Dynamics, Singapore: World Scientific.CrossRef
Luo, A.C.J., 2011, Regularity and Complexity in Dynamical Systems, New York: Springer.
Luo, A.C.J., 2012, Continuous Dynamical Systems, HEP/L&H Scientific, Beijing/Glen Carbon.MATH
Luo, A.C.J., 2019, On stability and bifurcation of equilibriums in nonlinear systems, Journal of Vibration Testing and System Dynamics, 3(2), pp. 147–232.CrossRef
Marsden, J.E. and McCracken, M.F., 1976, The Hopf Bifurcation and Its Applications, Applied Mathematical Science 19, Springer-Verlag, New York.
Metadata
Title
Stability of Equilibriums
Author
Albert C. J. Luo
Copyright Year
2019
Book
Bifurcation and Stability in Nonlinear Dynamical Systems

Print ISBN: 978-3-030-22909-2

Electronic ISBN: 978-3-030-22910-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-22910-8_1

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