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Weak tracking in nonautonomous chaotic systems.

Hassan Alkhayuon¹, Peter Ashwin²

¹School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland.

Physical Review. E

|December 17, 2020

Summary

This summary is machine-generated.

Rate-induced transitions in dynamical systems can lead to weak tracking, a phenomenon where a system

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Area of Science:

Dynamical Systems and Chaos Theory
Nonautonomous Systems Analysis

Background:

Previous studies explored rate-induced transitions in pullback attractors for systems with parameter shifts.
Transitions to equilibrium or periodic orbits were well-documented.
Transitions involving chaotic attractors were less understood.

Purpose of the Study:

Investigate rate-induced transitions for systems with chaotic attractors.
Identify and characterize a new phenomenon termed 'weak tracking'.
Determine conditions necessary for weak tracking.

Main Methods:

Analysis of nonautonomous systems with parameter shifts.
Demonstration using a nonautonomous Rössler system.
Identification of critical rates associated with weak tracking.

Main Results:

A new phenomenon, weak tracking, is identified.
Weak tracking occurs when a pullback attractor limits to a proper subset of a future chaotic attractor.
Infinitely many critical rates exist where the system tracks unstable periodic orbits.

Conclusions:

Weak tracking is a novel phenomenon in rate-induced transitions.
The study provides necessary conditions for weak tracking.
This research expands understanding of transitions to chaotic attractors.