Changes in the dynamical behavior of nonlinear systems induced by noise

Landa, P. S.; McClintock, Peter V. E.

doi:10.1016/s0370-1573(99)00043-5

Cited by 99 publications

(34 citation statements)

References 99 publications

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“…The development of theoretical and computational models of ratchet systems flourishes [35][36][37][38][39][40][41][42][43][44] and is essential for the design of new separation methods and the interpretation of experimental observations. One of the challenges encountered in describing the operation of real electrophoresis-based ratchets is the faithful representation of the field lines in microfabricated electrophoretic devices.…”

Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.

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Section: Ratchetsmentioning

confidence: 99%

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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“…(see, e.g., [24]). Even small random perturbations can result in substantial changes in the dynamics of a non linear system [25][26][27][28][29]. The following wide spectrum of phenomena related to the action of random distur bances is well known: stochastic resonance [30,31], noise induced transitions [26], noise induced sto chastic bifurcations [32,33], and noise assisted order [34,35] and chaos [36].…”

Section: Model For the Process With Random Fluctuationsmentioning

confidence: 99%

Solidification dynamics under random external-temperature fluctuations

et al. 2013

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Abstract-The nonlinear dynamic mechanisms of solid phase formation with a phase transition region are studied under periodic and random fluctuations of the cooling boundary temperature. It is theoretically shown that a mushy zone can form even at close liquid and cooling boundary temperatures due to random temperature field fluctuations. The growth of a solid phase with the mushy zone is investigated as a function of the autocovariance characteristics of random noises.

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“…Присутствие даже малых случайных возмуще-ний может привести к существенным изменениям в динамике системы [1,2,3,4]. Известен широкий круг явлений, связанных с воздействием случайных помех: стохастический ре-зонанс [5,6], индуцированные шумами переходы [2], порождаемый шумами порядок [7,8] и хаос [9].…”

Section: § 1 введениеunclassified

Backward stochastic bifurcations of the discrete system cycles

Bashkirtseva¹,

Ryashko²,

Fedotov³

et al. 2010

Nelin. Dinam.

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В работе рассматриваются стохастически возмущенные предельные циклы дискретных динамических систем в зоне удвоения периода. Исследуется явление обратных стохастиче-ских бифуркаций (ОСБ) -уменьшения кратности цикла при увеличении интенсивности шума. Предлагается метод анализа ОСБ на основе техники функции стохастической чув-ствительности. Конструктивные возможности данного метода демонстрируются на примере анализа ОСБ стохастических циклов систем Ферхюльста и Риккера.Ключевые слова: бифуркации, дискретные системы, модель Ферхюльста, стохастиче-ская чувствительность I. A. Bashkirtseva, L. B. Ryashko, S. P. Fedotov, I. N. Tsvetkov Backward stochastic bifurcations of the discrete system cycles We study stochastically forced limit cycles of discrete dynamical systems in a perioddoubling bifurcation zone. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Verhulst and Ricker systems are demonstrated.

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Changes in the dynamical behavior of nonlinear systems induced by noise

Cited by 99 publications

References 99 publications

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Solidification dynamics under random external-temperature fluctuations

Backward stochastic bifurcations of the discrete system cycles

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