Stability in the critical case and bifurcations in impulsive systems (Q2121941)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability in the critical case and bifurcations in impulsive systems |
scientific article |
Statements
Stability in the critical case and bifurcations in impulsive systems (English)
0 references
5 April 2022
0 references
A periodic impulsive system of the second order is studied. The conditions for the occurrence of the Andronov-Hopf bifurcation in the given system are discussed. Explicit formulas for calculating numerically the first Lyapunov value are derived. These formulas allow to determine the direction of the Andronov-Hopf bifurcation. The critical case of stability of the zero solution of the impulsive system is investigated. A scheme for reducing the polynomial mapping to normal form is suggested.
0 references
differential equations with impulses
0 references
periodicity
0 references
the critical case of stability
0 references
Andronov-Hopf bifurcation
0 references
0 references
0 references
0 references
