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Mathematics LibreTexts

8: Nonlinear Differential Equations

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We now turn our attention to nonlinear differential equations. In particular, we study how small changes in the parameters of a system can result in qualitative changes in the dynamics. These qualitative changes in the dynamics are called bifurcations. To understand bifurcations, we first need to understand the concepts of fixed points and stability.

Thumbnail: A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. (Public Domain; Catslash).


This page titled 8: Nonlinear Differential Equations is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform.

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