Bifurcation Diagrams

Thomas S. Parker and Leon O. Chua
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Thomas S. Parker: Hewlett Packard
Leon O. Chua: University of California, Department of Electrical Engineering and Computer Sciences

Chapter Chapter 8 in Practical Numerical Algorithms for Chaotic Systems, 1989, pp 201-235 from Springer

Abstract: Abstract Consider an nth-order continuous-time system (8.1) $$\dot x = f(x,a)$$ with a parameter α ∈ ℝ. As α changes, the limit sets of the system also change. Typically, a small change in α produces small quantitative changes in a limit set. For instance, perturbing α could change the position of a limit set slightly, and if the limit set is not an equilibrium point, its shape or size could also change. There is also the possibility that a small change α a can cause a limit set to undergo a qualitative change. Such a qualitative change is called abifurcation and the value of α at which a bifurcation occurs is called a bifurcation value.

Keywords: Equilibrium Point; Hopf Bifurcation; Bifurcation Diagram; Bifurcation Point; Pitchfork Bifurcation (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4612-3486-9_8

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