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- W57331505 abstract "The goal of this chapter is to introduce the concept of linearization near an equilibrium point of a nonlinear system. This process substitutes a linear system for a nonlinear system, at least near an equilibrium point. An equilibrium point is hyperbolic if all of the eigenvalues of the linearized system have nonzero real parts. In the hyperbolic case, the flow of the nonlinear system is locally conjugate to the flow of the linearized system near the equilibrium point. In particular, this allows us to prove the Stable Curve Theorem, which produces solution curves tending to and from an equilibrium in the saddle case. This also introduces the notion of stability. We describe the notion of asymptotic stability of equilibria and then investigate bifurcations that occur near equilibria, specifically the saddle-node bifurcation." @default.
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- W57331505 date "2013-01-01" @default.
- W57331505 modified "2023-09-23" @default.
- W57331505 title "Equilibria in Nonlinear Systems" @default.
- W57331505 doi "https://doi.org/10.1016/b978-0-12-382010-5.00008-7" @default.
- W57331505 hasPublicationYear "2013" @default.
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