Periodic solutions of systems of ordinary differential equations which approximate delay equations (Q752295)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Periodic solutions of systems of ordinary differential equations which approximate delay equations |
scientific article; zbMATH DE number 4177642
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic solutions of systems of ordinary differential equations which approximate delay equations |
scientific article; zbMATH DE number 4177642 |
Statements
Periodic solutions of systems of ordinary differential equations which approximate delay equations (English)
0 references
1988
0 references
We study a very simple approximation scheme for \[ (1)\quad \dot x(t)=- \alpha f(x(t-1)),\quad t\geq 0,\quad x(t)=\phi (t),\quad -1\leq t\leq 0, \] where \(\alpha >0\) and f:R\(\to R\), and demonstrate that the approximating ordinary differential systems inherit from (1) the occurence of Hopf bifurcations and the existence of global branches of nontrivial periodic solutions.
0 references
Hopf bifurcations
0 references
global branches of nontrivial periodic solutions
0 references
