Quasiperiodicity and suppression of multistability in nonlinear dynamical systems

Lai, Ying Cheng; Grebogi, Celso

doi:10.1140/epjst/e2017-70062-0

Cited by 20 publications

(11 citation statements)

References 151 publications

(214 reference statements)

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“…For γ > γ t p , there are three steady states in the system: two stable and one unstable, where the lowabundance stable state is a continuation of the extinction state from γ < γ t p , and the high-abundance stable state and the unstable states are created at the saddle-node bifurcation. There is then multistability [71][72][73][74][75][76][77][78][79] in the system in that there are two attractors in the system for γ > γ t p , each with its own basin of attraction. In general, the boundary separating the two basins of attraction is the stable manifold of the unstable steady state [80,81].…”

Section: B Theoretical Understanding Of the Scaling Lawmentioning

confidence: 99%

Noise-enabled species recovery in the aftermath of a tipping point

et al. 2020

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The beneficial role of noise in promoting species coexistence and preventing extinction has been recognized in theoretical ecology, but previous studies were mostly concerned with low-dimensional systems. We investigate the interplay between noise and nonlinear dynamics in real-world complex mutualistic networks with a focus on species recovery in the aftermath of a tipping point. Particularly, as a critical parameter such as the mutualistic interaction strength passes through a tipping point, the system collapses and approaches an extinction state through a dramatic reduction in the species populations to near-zero values. We demonstrate the striking effect of noise: when the direction of parameter change is reversed through the tipping point, noise enables species recovery which otherwise would not be possible. We uncover an algebraic scaling law between the noise amplitude and the parameter distance from the tipping point to the recovery point and provide a physical understanding through analyzing the nonlinear dynamics based on an effective, reduced-dimension model. Noise, in the form of small population fluctuations, can thus play a positive role in protecting high-dimensional, complex ecological networks.

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Section: B Theoretical Understanding Of the Scaling Lawmentioning

confidence: 99%

Noise-enabled species recovery in the aftermath of a tipping point

et al. 2020

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“…Note that, not all stable two-cluster states can be observed in a globally coupled system of finite size. In such a system, multistability [65][66][67][68][69][70][71][72][73][74] is common, and the basin of attraction of a stable attractor can have a fractal structure, on which small perturbations can have a significant effect. Certain states are thus not physically observable.…”

Section: Globally Coupled Mapsmentioning

confidence: 99%

Transition to high-dimensional chaos in nonsmooth dynamical systems

Lai

2018

Phys. Rev. E

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We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors in between the regimes of low-and high-dimensional chaos. That is, the emergence of high-dimensional chaos is preceded by the system's settling into a totally nonchaotic regime. This is characteristically distinct from the situation in smooth dynamical systems where high-dimensional chaos emerges directly and smoothly from low-dimensional chaos. We carry out an analysis to elucidate the underlying mechanism for the abrupt emergence and disappearance of the periodic attractors and provide strong numerical support for the typicality of the transition route in the pertinent two-dimensional parameter space. The finding has implications to applications where high-dimensional and robust chaos is desired.

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“…Need for the latter arose because some researchers seemed to remain unpersuaded by the arguments in the Letter 37 and had been explicitly 38,71,72 or implicitly 39,41 continuing to refer to the original conjecture 19,21 of chaotic diffusion as the mechanism underlying the resonant enhancement of electron transport. It also seems that a huge number of references to this exciting-sounding but incorrect idea done before the publication of the Letter 37 and its continued promulgation 38,39,41,71,72 after it keep misleading researchers in other areas [73][74][75][76][77][78][79] , who still mention the resonant enhancement of electron drift 19,21,26 as a manifestation of "chaotic dynamics in semiconductor SLs" 73,75,76,78,79 or as the ability of non-KAM chaos to "enhance electronic transport in semiconductor superlattices" 74,77 .…”

Section: Introductionmentioning

confidence: 99%

Mechanism of resonant enhancement of electron drift in nanometer semiconductor superlattices subjected to electric and inclined magnetic fields

Soskin¹,

Khovanov²,

McClintock³

2019

Phys. Rev. B

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We address the increase of electron drift velocity that arises in semiconductor superlattices (SLs) subjected to constant electric and magnetic fields. It occurs if the magnetic field possesses nonzero components both along and perpendicular to the SL axis and the Bloch oscillations along the SL axis become resonant with cyclotron rotation in the transverse plane. It is a phenomenon of considerable interest, so that it is important to understand the underlying mechanism. In an earlier Letter (Phys. Rev. Lett. 114, 166802 (2015)) we showed that, contrary to a general belief that drift enhancement occurs through chaotic diffusion along a stochastic web (SW) within semiclassical collisionless dynamics, the phenomenon actually arises through a non-chaotic mechanism. In fact, any chaos that occurs tends to reduce the drift. We now provide fuller details, elucidating the mechanism in physical terms, and extending the investigation. In particular, we: (i) demonstrate that pronounced drift enhancement can still occur even in the complete absence of an SW; (ii) show that, where an SW does exist and its characteristic slow dynamics comes into play, it suppresses the drift enhancement even before strong chaos is manifested; (iii) generalize our theory for non-small temperature, showing that heating does not affect the enhancement mechanism and accounting for some earlier numerical observations; (iv) demonstrate that certain analytic results reported previously are incorrect; (v) provide an extended critical review of the subject and closely related issues; and (vi) discuss some challenging problems for the future.

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Quasiperiodicity and suppression of multistability in nonlinear dynamical systems

Cited by 20 publications

References 151 publications

Noise-enabled species recovery in the aftermath of a tipping point

Noise-enabled species recovery in the aftermath of a tipping point

Transition to high-dimensional chaos in nonsmooth dynamical systems

Mechanism of resonant enhancement of electron drift in nanometer semiconductor superlattices subjected to electric and inclined magnetic fields

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