Bifurcation and stability of neutral systems near third-order resonance
Abstract
In the present paper, an autonomous system of differential equations which depends on a certain parameter is analyzed under the assumption that in the region of bifurcation values of this parameter, the linear portion of the system possesses several pairs of pure imaginary eigenvalues which, at the resonance point of the parameter, are linked by means of a third-order resonance relation. Criteria for strong instability are derived, and cases where the stability properties bifurcate are identified.
- Publication:
-
Prikladnaia Matematika i Mekhanika
- Pub Date:
- June 1979
- Bibcode:
- 1979PriMM..43..429G
- Keywords:
-
- Branching (Mathematics);
- Differential Equations;
- Numerical Stability;
- Resonance;
- Systems Stability;
- Asymptotic Methods;
- Matrices (Mathematics);
- Nonlinearity;
- Perturbation Theory;
- Resonant Frequencies;
- Physics (General)