On–off intermittency and coherent bursting in stochastically-driven coupled maps

Metta, Sabino; Provenzale, A.; Spiegel, E. A.

doi:10.1016/j.chaos.2010.06.001

Cited by 17 publications

(13 citation statements)

References 18 publications

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“…In figure 3(b), we can see higher values of kurtosis in the area very close to stability curve. As suggested by previous research (Metta et al 2010), there is on-off intermittency in the Ricker Map of the unstable region in parameter space and very near the stability curve.…”

Section: Single Ricker Mapmentioning

confidence: 75%

2010 program of study : swirling and swimming in turbulence

Balmforth¹,

Thiffeault²

2011

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Section: Single Ricker Mapmentioning

confidence: 75%

2010 program of study : swirling and swimming in turbulence

Balmforth¹,

Thiffeault²

2011

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“…According to figure 2, on-off intermittency emerges only for certain choices of r 0 and σ. Metta et al (2010) suggested a method to find on-off intermittency by first computing the stability curve in a parameter space which consists of the mean value of the parameter and the intensity of the noise. They then used kurtosis to locate on-off intermittency in the parameter space.…”

Section: Single Ricker Mapmentioning

confidence: 99%

On-off Intermittency in Locally Coupled Maps

Moon¹

2010

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On-off intermittency refers to the special pattern of time series which experience long time periods of calm behavior followed by short periods at bursting. In particular, the Ricker Map, which is a model of the discrete evolution of the expected population of one species at a given generation, is implemented to generate on-off intermittency. The on-off intermittency generated by the Ricker Map also exhibits the main characteristics found in other dynamical systems. On-off intermittency in a locally connected Ricker Map is the main focus here. The signal transfer between adjacent maps changes the stability condition compared with that of a single map, which leads to different conditions for on-off intermittency in locally coupled Ricker maps. The evolution and signal transfer in locally connected maps is carefully studied using a simple continuous model which contains similar structure and generates on-off intermittency. Through this analysis, it is found that a specific map in a locally connected structure recieves positively correlated signals from the adjacent maps, which generates more on-stages compared with a single map which has the same parameters.

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“…and thus we get the Lyapunov exponent [35] Figure 4 depicts the normalized frequency of synchronization F (λ < 0) for system of two passively coupled cells (eqs. (1) and (4)), as a function of cell affinity , averaged over all values of the coupling parameter and logistic parameter .…”

Section: Observational Heterarchy and Biochemical Substance Exchange mentioning

confidence: 99%

A numerical study of synchronization in the process of biochemical substance exchange in a diffusively coupled ring of cells

2013

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Abstract:In this paper we numerically investigate a model of a diffusively coupled ring of cells. To model the dynamics of individual cells we propose a map with cell affinity, which is a generalization of the logistic map. First, the basic features of a one-cell system are studied in terms of the Lyapunov exponent, Kolmogorov complexity and Sample Entropy. Second, the notion of observational heterarchy, which is a perpetual negotiation process between different levels of the description of a phenomenon, is reviewed. After these preliminaries, we study how the active coupling induced by the consideration of the observational heterarchy modifies the synchronization property of the model with N=100 cells. It is shown numerically that the active coupling enhances synchronization of biochemical substance exchange in several different conditions of cell affinity. PACS

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On–off intermittency and coherent bursting in stochastically-driven coupled maps

Cited by 17 publications

References 18 publications

2010 program of study : swirling and swimming in turbulence

2010 program of study : swirling and swimming in turbulence

On-off Intermittency in Locally Coupled Maps

A numerical study of synchronization in the process of biochemical substance exchange in a diffusively coupled ring of cells

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