Weak tracking in nonautonomous chaotic systems
Loading...
Files
Published version
Date
2020-11-19
Authors
Alkhayuon, Hassan
Ashwin, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Published Version
Abstract
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to “parameter shifts” between two asymptotically steady values of a system parameter. For cases where the attractors limit to equilibrium or periodic orbit in past and future limits of such an nonautonomous systems, these can occur as the parameter change passes through a critical rate. Such rate-induced transitions for attractors that limit to chaotic attractors in past or future limits has been less examined. In this paper, we identify a new phenomenon is associated with more complex attractors in the future limit: weak tracking, where a pullback attractor of the system limits to a proper subset of an attractor of the future limit system. We demonstrate weak tracking in a nonautonomous Rössler system, and argue there are infinitely many critical rates at each of which the pullback attracting solution of the system tracks an embedded unstable periodic orbit of the future chaotic attractor. We also state some necessary conditions that are needed for weak tracking.
Description
Keywords
Chaotic systems , Chaotic attractors , Induced transitions , Non-autonomous system , Nonautonomous chaotic systems , Parameter changes , Parameter shifts , Pullback attractors , Unstable periodic orbits
Citation
Alkhayuon, H. and Ashwin, P. (2020) 'Weak tracking in nonautonomous chaotic systems', Physical Review E, 102 (5), 052210 (7 pp). doi: 10.1103/PhysRevE.102.052210
Link to publisher’s version
Collections
Copyright
© 2020 American Physical Society