One-Parameter Bifurcations of Equilibria in Continuous-Time Systems
In this chapter we formulate conditions defining the simplest bifurcations of equilibria in n-dimensional continuous-time systems: the fold and the Hopf bifurcations. Then we study these bifurcations in the lowest possible dimensions: the fold bifurcation for scalar systems and the Hopf bifurcation for planar systems. Chapter 5 shows how to “lift” these results to n-dimensional situations.
KeywordsNormal Form Hopf Bifurcation Phase Portrait Nondegeneracy Condition Bibliographical Note
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