Dynamical Systems and Bifurcations
In this section we develop the rudiments of the modern theory of dynamical systems. To give the reader a bird’s eye view of this exciting field, we will for the most part skip the proofs. Some results are identical in ℝ n to those stated in ℝ2 in Chapter 2, but the center manifold theorem and bifurcation calculations are new in this chapter. We will also use machinery that we have built up enroute to this chapter to sharpen statements made in Chapter 2. Readers who wish to consult more detailed books are referred to Guckenheimer and Holmes , Ruelle , or Wiggins .
KeywordsPeriodic Orbit Equilibrium Point Hopf Bifurcation Bifurcation Diagram Unstable Manifold
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