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- Title
Noninvasive Stabilization of Periodic Orbits in -Symmetrically Coupled Systems Near a Hopf Bifurcation Point.
- Authors
Hooton, Edward; Balanov, Zalman; Krawcewicz, Wieslaw; Rachinskii, Dmitrii
- Abstract
Pyragas time-delayed feedback control has proven itself as an effective tool to noninvasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings. In this paper, we consider -symmetric systems of van der Pol and optical oscillators coupled in a cube-like configuration. These systems undergo equivariant Hopf bifurcations giving rise to multiple branches of unstable periodic solutions. We introduce a delayed control term, which ensures stabilization of a selected branch. Group theoretic restrictions which help to shape our choice of control are discussed. Furthermore, we explicitly describe the domains in a two-dimensional parameter space for which the periodic solutions of the delayed system are stable.
- Subjects
SPATIOTEMPORAL processes; EXTERIOR differential systems; STABILITY theory; HOPF bifurcations; EQUILIBRIUM
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2017, Vol 27, Issue 6, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127417500870