Study on Critical Conditions and Transient Behavior in Noise-Induced Bifurcations

Li, Zigang; Guo, Kongming; Hong, Li

doi:10.1007/978-3-319-28028-8_9

Cited by 2 publications

(3 citation statements)

References 24 publications

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“…Therefore, condition ( 13) implies the case Γ→C 3 . Such a scenario has neither been documented in Figure 4 nor in Figure 5 since the noise intensity chosen for the numerical experiments (ε = 0.1) is simply too small to satisfy condition (13).…”

Section: 2mentioning

confidence: 95%

“…In response to small perturbations, we expect the resulting random consumption trajectories to leave the deterministic attractor(s) and be randomly distributed around it (them), i.e. spend most of the time in a neighborhood of some attractor ( [13]). In this first approach to the stochastic case, we report outcomes of numerical experiments involving two types of noise.…”

Section: 2mentioning

confidence: 99%

“…9 In the related literature, our problem of describing transition behavior, is framed as the search for a most probable escape path (MPEP). For examples, see [17], [13] or [19]. For a few systems it has been possible to solve the problem analytically.…”

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confidence: 99%

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Transitions between metastable long-run consumption behaviors in a stochastic peer-driven consumer network

Jungeilges¹,

Nilssen²,

Perevalova³

et al. 2021

DCDS-B

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<p style='text-indent:20px;'>We study behavioral change - as a transition between coexisting attractors - in the context of a stochastic, non-linear consumption model with interdependent agents. Relying on the indirect approach to the analysis of a stochastic dynamic system, and employing a mix of analytical, numerical and graphical techniques, we identify conditions under which such transitions are likely to occur. The stochastic analysis depends crucially on the stochastic sensitivity function technique as it can be applied to the stochastic analoga of closed invariant curves [<xref ref-type="bibr" rid="b14">14</xref>], [<xref ref-type="bibr" rid="b1">1</xref>]. We find that in a moderate noise environment increased peer influence actually reduces the complexity of observable long-run consumer behavior.</p>

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Section: 2mentioning

confidence: 95%

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

Transitions between metastable long-run consumption behaviors in a stochastic peer-driven consumer network

Jungeilges¹,

Nilssen²,

Perevalova³

et al. 2021

DCDS-B

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Studying the Global Bifurcation Involving Wada Boundary Metamorphosis by a Method of Generalized Cell Mapping with Sampling-Adaptive Interpolation

Liu

Hong

Tang

2018

Int. J. Bifurcation Chaos

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In this paper, a new method of Generalized Cell Mapping with Sampling-Adaptive Interpolation (GCMSAI) is presented in order to enhance the efficiency of the computation of one-step probability transition matrix of the Generalized Cell Mapping method (GCM). Integrations with one mapping step are replaced by sampling-adaptive interpolations of third order. An explicit formula of interpolation error is derived for a sampling-adaptive control to switch on integrations for the accuracy of computations with GCMSAI. By applying the proposed method to a two-dimensional forced damped pendulum system, global bifurcations are investigated with observations of boundary metamorphoses including full to partial and partial to partial as well as the birth of fully Wada boundary. Moreover GCMSAI requires a computational time of one thirtieth up to one fiftieth compared to that of the previous GCM.

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Study on Critical Conditions and Transient Behavior in Noise-Induced Bifurcations

Cited by 2 publications

References 24 publications

Transitions between metastable long-run consumption behaviors in a stochastic peer-driven consumer network

Transitions between metastable long-run consumption behaviors in a stochastic peer-driven consumer network

Studying the Global Bifurcation Involving Wada Boundary Metamorphosis by a Method of Generalized Cell Mapping with Sampling-Adaptive Interpolation

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