Transient chaos in time-delayed systems subjected to parameter drift

Cantisán, Julia; Seoane, Jesús M.; Sanjuán, Miguel A. F.

doi:10.1088/2632-072x/abd67b

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…Systems subjected to parameter drift are of general interest. Cantisán et al [17] study the case of a time-delayed oscillator whose time delay varies at a non-negligible rate. They consider a scenario where the time delay is constant at the beginning and end of the observation and increases linearly in the middle.…”

Section: Systems Subjected To Nonrecurrent Parameter Driftmentioning

confidence: 99%

Focusing on transient chaos

Omel’chenko¹,

Tél²

2022

J. Phys. Complex.

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Recent advances in the field of complex, transiently chaotic dynamics are reviewed, based on the results published in the focus issue of J. Phys. Complex. on this topic. One group of achievements concerns network dynamics where transient features are intimately related to the degree and stability of synchronization, as well as to the network topology. A plethora of various applications of transient chaos are described, ranging from the collective motion of active particles, through the operation of power grids, cardiac arrhythmias, and magnetohydrodynamical dynamos, to the use of machine learning to predict time evolutions. Nontraditional forms of transient chaos are also explored, such as the temporal change of the chaoticity in the transients (called doubly transient chaos), as well as transients in systems subjected to parameter drift, the paradigm of which is climate change.

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Section: Systems Subjected To Nonrecurrent Parameter Driftmentioning

confidence: 99%

Focusing on transient chaos

Omel’chenko¹,

Tél²

2022

J. Phys. Complex.

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“…If a plausible picture is needed behind the snapshot view, we can speak of the theory of parallel dynamical evolutions of the systems, in analogy with parallel climate realizations. A recent effort in this direction is the application of the snapshot view to epidemics under changing environmental conditions [51], to aperiodically driven Hamiltonian systems [38,39], to tipping phenomena [7,47], and to advection in open flows of changing intensity [81].…”

Section: Introductionmentioning

confidence: 99%

Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

2021

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We argue that typical mechanical systems subjected to a monotonous parameter drift whose timescale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed—in analogy with the real climate—by monitoring parallel dynamical evolutions originating from different initial conditions. To this end an ensemble view is needed, enabling one to compute ensemble averages characterizing the instantaneous state of the system. We illustrate this on the examples of (i) driven dissipative and (ii) Hamiltonian systems and of (iii) non-driven dissipative ones. We show that in order to find the most transparent view, attention should be paid to the choice of the initial ensemble. While the choice of this ensemble is arbitrary in the case of driven dissipative systems (i), in the Hamiltonian case (ii) either KAM tori or chaotic seas should be taken, and in the third class (iii) the best choice is the KAM tori of the dissipation-free limit. In all cases, the time evolution of the chosen ensemble on snapshots illustrates nicely the geometrical changes occurring in the phase space, including the strengthening, weakening or disappearance of chaos. Furthermore, we show that a Smale horseshoe (a chaotic saddle) that is changing in time is present in all cases. Its disappearance is a geometrical sign of the vanishing of chaos. The so-called ensemble-averaged pairwise distance is found to provide an easily accessible quantitative measure for the strength of chaos in the ensemble. Its slope can be considered as an instantaneous Lyapunov exponent whose zero value signals the vanishing of chaos. Paradigmatic low-dimensional bistable systems are used as illustrative examples whose driving in (i, ii) is chosen to decay in time in order to maintain an analogy with case (iii) where the total energy decreases all the time.

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Rate and memory effects in bifurcation-induced tipping

et al. 2023

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A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.

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Transient chaos in time-delayed systems subjected to parameter drift

Cited by 5 publications

References 19 publications

Focusing on transient chaos

Focusing on transient chaos

Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

Rate and memory effects in bifurcation-induced tipping

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