Basic Nonlinear Phenomena
Beginning with this chapter, nonlinearity and parameter dependence willplay a crucial role. We shall assume throughout that λ is a real parameter, and we shall study solutions of a system of ODEs, or solutions of a system of “algebraic” equations, Sometimes boundary conditions must be attached to equation (2.1). As in Chapter 1, the vectors y and f have n components. If a particular example involves more than one parameter, we assume for the time being that all except λ are kept fixed. Clearly, solutions y of equation (2.1) or (2.2) in general vary with λ. We shall assume throughout that f depends smoothly on y and λ—that is, f is to be sufficiently often continuously differentiable. This hypothesis is usually met by practical examples.
KeywordsPeriodic Orbit Hopf Bifurcation Bifurcation Diagram Bifurcation Point Homoclinic Orbit
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