Effects of time delay on symmetric two-species competition subject to noise

Nie, Linru; Mei, Dong-Cheng

doi:10.1103/physreve.77.031107

Cited by 72 publications

(34 citation statements)

References 44 publications

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“…A single-mode laser cubic model driven by quadratic pump noise was investigated by Cao and Wu, and the same phenomenon was found at the boundary I = 0 [61]. Further, this phenomenon was found in a two-dimensional dynamic system [46].…”

Section: The Euler Differential Equation Of General Time-delayed Modelmentioning

confidence: 77%

“…Rosenblum and Pikovsky suggested that time-delayed feedback can be used for the purposes of deep brain stimulation such as suppression of pathological brain rhythms [44]. Nie and Mei displayed that a time delay can suppress a population explosion [45], synchronous oscillation, a first-order-like transition and the nonmonotonic behavior of the characteristic correlation time caused by the time delay [46] in the Lotka-Volterra model. It was found that a longer time delay results in a less stable system of the predator-prey-type ecosystem [47] by Cai and Lin.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence of strong noise on the decline and propagation of population in the delayed Malthus–Verhulst model

Cai

Mei

2010

Physica A: Statistical Mechanics and its Applications

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Section: The Euler Differential Equation Of General Time-delayed Modelmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Influence of strong noise on the decline and propagation of population in the delayed Malthus–Verhulst model

Cai

Mei

2010

Physica A: Statistical Mechanics and its Applications

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“…The effects of time delay in competitive systems in the ecological field have been also studied. The results imply that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems [8]. The delay time also induces stochastic oscillations in gene regulation [9].…”

mentioning

confidence: 88%

Stochastic tumor growth system with two different kinds of time delay

Chun-sheng

Wang

2011

Open Physics

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Abstract:The dynamical properties of a noise-driven tumor cell growth system are investigated when there exist two different kinds of time delays, in the deterministic and fluctuating forces, respectively. Using the approximation probability density approach, the delayed Fokker-Planck equation is obtained. The effects of two different time delays on the stationary probability distribution (SPD), the mean value and the mean passage time (MFPT) are discussed. It is found that the time delay τ 1 in the deterministic force can enhance tumor cell number, while the time delay In recent years, time-delayed stochastic processes have been the subject of increased interest in various fields. It was recently found that noise and delay can actually be an integral part of biological information processing [1,2]. Mainly, bistable systems with simultaneous noise and time delay have been investigated in detail. Ref.[3] founds noise induced resonance in delayed feedback systems. The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise has been studied analytically and numerically [4]. The noise-induced dynamics of a prototypical bistable system with delayed feedback have been studied theoretically and numerically [5]. Wu investigated the phe- * E-mail: cjwangbj@126.com nomenon of stochastic resonance in a bistable system with time-delayed feedback driven by non-Gaussian noise [6]. Biological systems subjected to simultaneous noise and time delay have especially attracted interest. For example, the effects of time delay on a mutualism system has been studied and it was found that the combination of the noise and the time delay completely suppresses population explosion [7]. The effects of time delay in competitive systems in the ecological field have been also studied. The results imply that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems [8]. The delay time also induces stochastic oscillations in gene regulation [9]. In many cases, the delay reflects transmission times related to the transport of matter, energy, and information through a system.The dynamical character of a tumor cell growth system subjected to a noise disturbance, which is described by 616 Unauthenticated Download Date | 5/11/18 6:53 AM

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“…For this phenomenon, according to Ref. [50], it implies that coherence resonance phenomenon with respect to non-Gaussian noises occurs in cytosol. Recently, coherence resonance has been studied in the twodimensional system [51][52][53][54].…”

Section: Naf and Cct Of Intracellular Ca 2+ Concentrationmentioning

confidence: 99%