The joy of transient chaos

Tél, Tamás

doi:10.1063/1.4917287

Cited by 87 publications

(35 citation statements)

References 73 publications

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“…This is an example of super-transient behavior, which is encountered in a rage of other systems and often have a mean transient time that scales exponentially with a system parameter. This has been observed for spatially extended systems [51][52][53][54][55][56], networks [38,57,58], and time-delay systems [39]. The observed behavior also shows similarities to stable chaos in coupled map lattices for which the transient time scales with the size of the lattice [59].…”

Section: B Scaling and Distribution Of Transient Durationsmentioning

confidence: 76%

Transient dynamics and their control in time-delay autonomous Boolean ring networks

et al. 2017

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Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation. To address this issue, we we have developed an experimental testbed to realize a time-delay autonomous Boolean network with three inhibitory nodes, known as a repressilator, and use it to study the dynamics that arise as time delays along the links vary. We observe various nearly-periodic oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay, and which are distinct from the eventual asymptotically stable periodic attractors. For repeated experiments with a given network, we find that stochastic processes give rise to a broad distribution of transient times with an exponential tail. In some cases, the transients are so long that it is doubtful the attractors will ever be approached in a biological system that has a finite lifetime. To counteract the long transients, we show experimentally that small, occasional perturbations applied to the time delays can force the trajectories to rapidly approach the attractors.

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Section: B Scaling and Distribution Of Transient Durationsmentioning

confidence: 76%

Transient dynamics and their control in time-delay autonomous Boolean ring networks

et al. 2017

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“…That means that two trajectories that start arbitrary close can finish in a different direction in the asymptotic region. This phenomenon is called chaotic scattering and is a kind of transient chaos [32,33]. The chaotic scattering is a common phenomenon in the open Hamiltonian system.…”

Section: Periodic Orbits and Their Stable And Unstable Manifoldsmentioning

confidence: 99%

Revealing roaming on the double Morse potential energy surface with Lagrangian descriptors

Montoya

Wiggins

2020

J. Phys. A: Math. Theor.

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In this paper, we analyse the phase space structure of the roaming dynamics in a two degree of freedom potential energy surface consisting of two identical planar Morse potentials separated by a distance. This potential energy surface was previously studied in [1], and it has two potential wells surrounded by an unbounded flat region containing no critical points. We study the phase space mechanism for the transference between the wells using the method of Lagrangian descriptors.

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“…Their lifetime strongly depends on the initial conditions in the deterministic case. In contrast to classical chimeras [20,21] or transient chaos in spatially extended systems [22,23], where the transient time exponentially increases with the system size, for amplitude chimeras the transient time decreases and saturates for large system size [24]. Thus, the transient nature of amplitude chimeras cannot be related to a finite size effect.…”

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confidence: 93%

Stability of amplitude chimeras in oscillator networks

Tumash¹,

Zakharova²,

Lehnert³

et al. 2017

EPL

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-We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size N = 12 exhibiting amplitude chimeras.Introduction. -The dynamical state of networks of homogeneously coupled identical elements can show a peculiar behavior by self-organizing into two spatially separated domains with dramatically different behavior, e.g. a spatially coherent and a spatially incoherent region. This phenomenon was named chimera state by Abrams and Strogatz [1] after the Greek fire-breathing monster, whose body consists of different animals. These hybrid states were discovered for phase oscillators in the early 2000's by Kuramoto and Battogtokh [2]. They observed a spontaneous breakup of the system into spatially coexisting synchronized and desynchronized domains with respect to the phase.Chimera states have possible applications to neural activity [3,4], heart fibrillation [5] and social systems [6]. Chimera states were also associated with such phenomena as epileptic seizure [7] and unihemispheric sleep, which has been detected for some sea mammals and birds [8]. These creatures can sleep with only one half of their brain while the other half remains awake. For instance, this enables sleeping dolphins to detect predators and migrant birds can travel for hundreds of kilometers without having a break [9]. Recently, unihemispheric sleep has been found also for humans [10].Chimera states were initially found for coupled phase oscillators, where coherence is related to phase-and frequency-locked oscillators and incoherence is associated with drifting oscillators. Since then numerous chimera

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The joy of transient chaos

Cited by 87 publications

References 73 publications

Transient dynamics and their control in time-delay autonomous Boolean ring networks

Transient dynamics and their control in time-delay autonomous Boolean ring networks

Revealing roaming on the double Morse potential energy surface with Lagrangian descriptors

Stability of amplitude chimeras in oscillator networks

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