Vol. 112, No. 1, 1984

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ISSN: 0030-8730
Iterated averaging for periodic systems with hidden multiscale slow times

Stephen C. Persek

Vol. 112 (1984), No. 1, 211–236

General asymptotic methods on various time scales are developed for periodic systems of ordinary differential equations in order to treat global motion in multi-oscillatory systems. Moreover, we show that bifurcations of an attractive and essentially nonperiodic nature can arise in systems that also possess several (often unstable) Hopf bifurcations. Such attractor bifurcations frequently dominate the long term system behavior. In addition, the methods here can be used to determine the flow on a center manifold in cases where center manifold theory indicates an instability at the origin of that manifold and little else about the flow. Finally, various examples of mixed scale motion are treated.

Mathematical Subject Classification 2000
Primary: 34C29
Secondary: 58F14
Received: 11 January 1982
Published: 1 May 1984
Stephen C. Persek