Mitigating long transient time in deterministic systems by resetting

Ray, Arnob; Pal, A.; Ghosh, Dibakar; Dana, Syamal K.; Hens, Chittaranjan

doi:10.1063/5.0038374

Cited by 27 publications

(14 citation statements)

References 74 publications

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“…In all the aspects considered above, the diffusive motion intermittent by stochastic resetting was governed by the linear partial differential equations. As we know so far, the only exception to this rule is the non-linear dynamical system such as chaotic Lorenz model analyzed in the reference [77]. However, this dynamics have nothing to do with a diffusive motion.…”

Section: Introductionmentioning

confidence: 99%

Non-linear diffusion with stochastic resetting

Chelminiak

2021

Preprint

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Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a timeindependent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and other problems have been intensively studied in the case of ordinary diffusive processes during the last decade. In this paper we consider the influence of stochastic resetting on a diffusive motion modeled in terms of the non-linear differential equation. The reason for its non-linearity is the power-law dependence of the diffusion coefficient on the probability density function or, in another context, the concentration of particles. We first derive an exact formula for the mean squared displacement and show how it attains the steady-state value under the exponential resetting. Then, we analyse the steady-state properties of the probability density function. We also explore the first-passage properties for the non-linear diffusion affected by the exponential resetting and find the exact expressions for the survival probability, the mean firstpassage time and the optimal resetting rate, which minimizes the mean time needed for a particle to reach a pre-determined target. Finally, we find the universal property that the relative fluctuation in the mean first-passage time of optimally restarted non-linear diffusion is always equal to unity.

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Section: Introductionmentioning

confidence: 99%

Non-linear diffusion with stochastic resetting

Chelminiak

2021

Preprint

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“…Moreover, ignoring the underlying dynamics that a system may exhibit from its initial point to its long-term behavior keeps us oblivious to the nature of the evolution of the system. The dynamics that exists before reaching an asymptotic state is called the transient dynamics, and the time required for any trajectory of a system to reach the final attractor (asymptotic state) from the initial state is called the transient time [4][5][6]. In recent years, the statistics analysis of transient time has received a considerable attention due to its relevance in complex systems [7][8][9], climatic models [10,11], ecology [12][13][14][15][16] and dynamical networks [17,18], in general.…”

Section: Introductionmentioning

confidence: 99%

Multimodal distribution of transient time of predator extinction in a three-species food chain

Pattanayak¹,

Mishra²,

Dana³

et al. 2022

Preprint

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Studies of transient dynamics captures the time history of any dramatic changes in the dynamics of a system. The transient dynamics is investigated here in a classic ecological model of a bistable tritrophic food chain. All the species in the food chain either coexist or undergoes a partial extinction with the loss of predator after a transient time that depends upon the initial density of species populations. The distribution of transient time of extinction of the predator in response to initial states shows interesting pattern of inhomogeneity and anisotropy in the basin of predator-fee state. Precisely, the distribution shows a multimodal character when the initial points are near the basin boundary, and unimodal at locations far from the border. The distribution is also anisotropic in the sense that the number of modes depends on the direction from the basin location. We define two new metrics, viz., homogeneity index and local isotropic index to characterize the distinctive features of the distribution. The inhomogeneity of distribution reduces significantly with resource enrichment, however, a similar change in anisotropy is relatively low. We try to explain the origin of such multimodal distributions from the dynamical system perspectives and present its ecological implications.

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“…For example, unbinding events in a chemical reaction [39,40], cleavage in RNA polymerization [41] or dissociation kinetics of GTP-RhoA in cell contraction [42] can be understood as resetting events. The phenomena has been catalyzed even further since over the last decade, resetting has found overreaching applications in statistical physics [43][44][45][46][47][48][49][50][51][52], computer science [53,54], ecology [55][56][57], complex systems [58][59][60] operation research [61][62][63] and economics [64][65][66]. Recently, the field has also seen advancements in experiments [67][68][69].…”

Section: Introductionmentioning

confidence: 99%

First-passage Brownian functionals with stochastic resetting

Singh,

Pal

2022

Preprint

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We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A firstpassage functional is defined aswhere t f is the first-passage time of a reset Brownian process x(τ ), i.e., the first time the process crosses zero. In here, the particle is reset to x R > 0 at a constant rate r starting from x 0 > 0 and we focus on the following functionals:, and (iii) functionals of the form A n = ´tf 0 dτ [x(τ )] n with n > −2. For first two functionals, we analytically derive the exact expressions for the moments and distributions. Interestingly, the residence time moments reach minima at some optimal resetting rates. A similar phenomena is also observed for the moments of the functional A n . Finally, we show that the distribution of A n for large A n decays exponentially as ∼ exp (−A n /a n ) for all values of n and the corresponding decay length a n is also estimated. In particular, exact distribution for the first passage time under resetting (which corresponds to the n = 0 case) is derived and shown to be exponential at large time limit in accordance with the generic observation. This behavioural drift from the underlying process can be understood as a ramification due to the resetting mechanism which curtails the undesired long Brownian first passage trajectories and leads to an accelerated completion. We confirm our results to high precision by numerical simulations.

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Mitigating long transient time in deterministic systems by resetting

Cited by 27 publications

References 74 publications

Non-linear diffusion with stochastic resetting

Non-linear diffusion with stochastic resetting

Multimodal distribution of transient time of predator extinction in a three-species food chain

First-passage Brownian functionals with stochastic resetting

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