Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

Guo, Kongming

doi:10.1016/j.physleta.2014.07.004

Cited by 12 publications

(3 citation statements)

References 15 publications

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“…Further, the information of the system in the phase interval [0, 2π] is lost. Thus, in order to solve these problems and consider persistent fluctuation along the trajectory, a kind of 1/N-period stroboscopic map is introduced [25].…”

Section: /N-period Stroboscopic Mapmentioning

confidence: 99%

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Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Guo

2017

Entropy

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Abstract:A semi-analytical method is proposed to calculate stochastic quasi-periodic responses of limit cycles in non-equilibrium dynamical systems excited by periodic forces and weak random fluctuations, approximately. First, a kind of 1/N-stroboscopic map is introduced to discretize the quasi-periodic torus into closed curves, which are then approximated by periodic points. Using a stochastic sensitivity function of discrete time systems, the transverse dispersion of these circles can be quantified. Furthermore, combined with the longitudinal distribution of the circles, the probability density function of these closed curves in stroboscopic sections can be determined. The validity of this approach is shown through a van der Pol oscillator and Brusselator.

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Section: /N-period Stroboscopic Mapmentioning

confidence: 99%

“…Based on the recurrence relation (25), M i (i = 2, ..., kN) can be calculated and the dispersion character of any circle can be quantified. If the circle under analysis is Г m , the periodic points on it are x Гm , x Г(m + N) , x Г(m + 2N) , ...,x Г(m + (k − 1)N) .…”

Section: Transverse Distribution Of the Closed Curves In Stroboscopicmentioning

confidence: 99%

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Guo

2017

Entropy

Self Cite

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show abstract

“…sitivity function (SSF) technique has been successfully used for the analysis of various noise-induced phenomena: backward stochastic bifurcations [19], an excitement of neuron [20], an extinction of population [21], a suppression of noise-induced chaos [22]. An extension of SSF technique to non-autonomous dynamical systems has been presented in the recent paper [23].…”

Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay

Bashkirtseva

Ryashko

2014

Physics Letters A

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

Guo

Hong

2016

Understanding Complex Systems

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Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

Cited by 12 publications

References 15 publications

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay

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

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