Time-Delay Induced Reentrance Phenomenon in a Triple-Well Potential System Driven by Cross-Correlated Noises

Jia, Zheng

doi:10.1007/s10773-008-9797-8

Cited by 20 publications

(6 citation statements)

References 19 publications

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“…That is to say, the time delay may induce the regime shifts from the vegetated state to the unvegetated one. Physically, this delay-induced regime shift is a delay-induced transition that has been also observed in the other systems such as the parallel chemical reaction system [46]. In a word, our results show that time delay, internal and external fluctuations and their correlation are able to drive regime shifts in the groundwater-dependent plant ecosystem.…”

Section: Noise and Delay Induced Phenomena In Vegetation Dynamicssupporting

confidence: 81%

Noise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay

Jia¹,

Dong-Cheng²

2015

J. Stat. Mech.

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Groundwater-dependent ecosystems may exhibit nonlinear dynamics with bifurcations resulting from feedbacks with water table dynamics. In this paper, by stochastic simulations, the stationary probability distribution and the mean first passage time are investigated in a groundwater-dependent ecosystem under the influences of environmental fluctuations, seasonal rainfall oscillation and time delay. We investigate a variety of noise-induced behaviors affecting regime shifts between ecosystem states. The results indicate that the phenomena of regime shift, noise enhanced stability (NES) and resonant activation (RA) may emerge in the dynamics of phreatophyte vegetation. Moreover, we also show that the direction of regime shifts depends on the time delay and the cross-correlation between noises. The cross-correlation between noises, the time delay, and the periodic force play a significant role on the NES and RA phenomena.

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Section: Noise and Delay Induced Phenomena In Vegetation Dynamicssupporting

confidence: 81%

Noise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay

Jia¹,

Dong-Cheng²

2015

J. Stat. Mech.

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“…Examples include propagation delays in networks [24], laser arrays [25][26][27], electronic circuits [28], and neural systems [29][30][31]. Time-delayed nonlinear systems are found to show interesting dynamical phenomena such as novel bifurcations [32,33], amplitude death [34], strange nonchaotic attractors [35], hyperchaos [36], stochastic dynamics [37][38][39], excitation regeneration [40], reentrance phenomena [41,42], and patterns [43]. However, the effect of time delay on VR has not been studied systematically.…”

Section: Introductionmentioning

confidence: 99%

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

2011

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The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.

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“…The effect of time delay in the overdamped quintic oscillator in the presence of additive and multiplicative noises has been analyzed by Jia. 27 The occurrence of chaos has been studied in the parametrically driven triple-well system. 28 In the system ͑1͒ we show the occurrence of single and multiple resonances and through a theoretical approximation we determine the values of the control parameters , g, and ⍀ at which the vibrational resonance occurs.…”

Section: Introductionmentioning

confidence: 99%

Analysis of vibrational resonance in a quintic oscillator

Jeyakumari¹,

Chinnathambi²,

Rajasekar

et al. 2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We consider a damped quintic oscillator with double-well and triple-well potentials driven by both low-frequency force f cos (omega)t and high-frequency force g cos (Omega)t with Omega>>omega and analyze the occurrence of vibrational resonance. The response consists of a slow motion with frequency omega and a fast motion with frequency Omega. We obtain an approximate analytical expression for the response amplitude Q at the low-frequency omega. From the analytical expression of Q, we determine the values of omega and g (denoted as omega(VR) and g(VR)) at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. We show that for fixed values of the parameters of the system, as omega varies, resonance occurs at most one value of omega. When the amplitude g is varied we found two and four resonances in the system with double-well and triple-well cases, respectively. We present examples of resonance (i) without cross-well motion and (ii) with cross-well orbit far before and far after it. omega(VR) depends on the damping strength d while g(VR) is independent of d. Moreover, the effect of d is found to decrease the response amplitude Q.

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Time-Delay Induced Reentrance Phenomenon in a Triple-Well Potential System Driven by Cross-Correlated Noises

Cited by 20 publications

References 19 publications

Noise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay

Noise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Analysis of vibrational resonance in a quintic oscillator

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