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Published in:
Short Introduction to Stability Theory of Deterministic Functional Differential Equations Read chapter Read first chapter

2013 | OriginalPaper | Chapter

5. Stability of Systems with Nonlinearities

Author : Leonid Shaikhet

Published in: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Publisher: Springer International Publishing

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Abstract

In Chap. 5 stability of the zero solution and positive equilibrium points for nonlinear systems is studied. In particular, differential equations with nonlinearities in deterministic and stochastic parts are considered, differential equation with fractional nonlinearity. It is shown that investigation of stability in probability for nonlinear systems with the level of nonlinearity higher than one can be reduced to investigation of asymptotic mean square stability of the linear part of the considered nonlinear system. The obtained results are illustrated by 18 figures.

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previous chapter Stability of Linear Systems of Two Equations
next chapter Matrix Riccati Equations in Stability of Linear Stochastic Differential Equations with Delays
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Metadata
Title
Stability of Systems with Nonlinearities
Author
Leonid Shaikhet
Copyright Year
2013
Publisher
Springer International Publishing
Book
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Print ISBN: 978-3-319-00100-5

Electronic ISBN: 978-3-319-00101-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-319-00101-2_5