Nonlinear Oscillations in Equations with Delays.
Abstract
These lectures are concerned only with some aspects of bifurcation theory in the local theory of nonlinear oscillations in equations with delays; that is, behavior of solutions near an equilibrium. In particular, how the qualitative behavior of solutions change is shown as parameters vary. A detailed study of the local theory is important in order to know the types of solutions to expect in a global problem. Of course, there is no reason to only study local theory near an equilibrium. One should study how the qualitative behavior changes near any invariant set - for example, behavior near a periodic orbit, behavior near an orbit which connects a saddle point to itself, etc. More complicated behavior is expected near these large invariant sets. One can obtain invariant torii, homoclines points which exhibit a chaotic behavior, etc.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1978
- Accession Number
- ADA056745
Entities
People
- Jack K. Hale
Organizations
- Brown University