The objective of this chapter is to give some fundamental notions and results in the theory of dynamical systems as well as their bifurcations, which are important in the qualitative study of dynamical systems and are used in the other two chapters, so that readers can become familiar with those important underlying ideas without referring to other textbooks or articles. Since the other chapters mainly deal with vector fields, that is, continuous dynamical systems, the description of this chapter also places more emphasis on continuous dynamical systems than on discrete dynamical systems, although one section is devoted to these discrete systems.
KeywordsVector Field Periodic Orbit Equilibrium Point Homoclinic Orbit Center Manifold
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