Chaos in time delay systems, an educational review
arXiv:1901.04826 · doi:10.1016/j.physrep.2019.08.001
Abstract
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases. Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics? This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos. Special emphasis is placed on a structured representation that is straightforward to follow. Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.
References in corpus (14)
- Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
- Synchronizing distant nodes: a universal classification of networks
- Amplitude-phase coupling drives chimera states in globally coupled laser networks
- Spatio-temporal phenomena in complex systems with time delays
- Heterogeneity of time delays determines synchronization of coupled oscillators
- Pattern formation in systems with multiple delayed feedbacks
- Synchronization of networks of oscillators with distributed delay coupling
- Laminar Chaos
- Spatio-temporal complexity in dual delay nonlinear laser dynamics: chimeras and dissipative solitons
- Stochastic switching in delay-coupled oscillators
- Aging transition in systems of oscillators with global distributed-delay coupling
- Characteristic Lyapunov vectors in chaotic time-delayed systems
- Enhancing noise-induced switching times in systems with distributed delays
- Entrenched time delays versus accelerating opinion dynamics: are advanced democracies inherently unstable?
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