Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay

✍ Scribed by V.I. Yudovich

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 744 KB
• Volume: 62
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(98)00002-1

✦ Synopsis

For a dynamical system witJh cosymmetry, a study is made of the bifurcation in which a cycle branches off from an equilibrium in a continuous one-parameter family of equilibria, as the parameter passes through a critical value. Unlike the classical situation that occurs when the equiliibrium is isolated, a self-excited oscillatory mode generally branches off with delay relative to the parameter. Another characteristic difference is the possibility of supercritical branching of an unstable limit cycle.