Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay (Q2714633)
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scientific article; zbMATH DE number 1607050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay |
scientific article; zbMATH DE number 1607050 |
Statements
20 June 2001
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bifurcation
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delay in parameter
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Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay (English)
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In a Hilbert space \(H\) the differential equation with the parameter \(\Lambda\) NEWLINE\[NEWLINE \dot\theta = F(\theta,\lambda)\tag{1} NEWLINE\]NEWLINE is considered, where \(F: H\times \mathbb{R}\to H\) is an analytical operator with a skew symmetry \(L: H\to H\) which does not depend on \(\lambda\). The bifurcation of a cycle from the equilibrium is considered by means of the Lyapunov-Schmidt procedure. Stability conditions for equilibria and limiting cycles are established.
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