Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
In this chapter we introduce and discuss the following fundamental notions that will be used throughout the book: topological equivalence of dynamical systems and their classification, bifurcations and bifurcation diagrams, and topological normal forms for bifurcations. The last section is devoted to the more abstract notion of structural stability. In this chapter we will be dealing only with dynamical systems in the state space X = ℝ n .
KeywordsPhase Portrait Bifurcation Diagram Invariant Manifold Local Bifurcation Bibliographical Note
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