Planar Dynamical Systems
In the previous chapter, we saw several classical examples of planar (or 2 dimensional) nonlinear dynamical systems. We also saw that nonlinear dynamical systems can show interesting and subtle behavior and that it is important to be careful when talking about solutions of nonlinear differential equations. Before dedicating ourselves to the task of building up in detail the requisite mathematical machinery we will first study in semi-rigorous but detailed fashion the dynamics of planar dynamical systems; that is, systems with two state variables. We say semi-rigorous because we have not yet given precise mathematical conditions under which a system of differential equations has a unique solution and have not yet built up some necessary mathematical prerequisites. These mathematical prerequisites are deferred to Chapter 3.
KeywordsEquilibrium Point Phase Portrait Josephson Junction Closed Orbit Saddle Node Bifurcation
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