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Spatiotemporal Bounded Noises and Their Application to the Ginzburg–Landau Equation

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Abstract

In this work, we introduce three spatiotemporal colored bounded noises, based on the zero-dimensional Cai–Lin, Tsallis–Borland, and sine-Wiener noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter τ and a spatial coupling parameter λ. In particular, we found that varying λ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim to investigate the role played by bounded noises on spatially extended nonlinear dynamical systems, we analyze the behavior of the real Ginzburg–Landau time-varying model additively perturbed by such noises. The observed phase transitions phenomenology is quite different from the one observed when the perturbations are unbounded. In particular, we observed inverse “order-to-disorder” transitions, and reentrant transitions, with dependence on the specific type of bounded noise.

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Acknowledgements

This research was performed under the partial support of the Integrated EU project P-medicine—From data sharing and integration via VPH models to personalized medicine (Project No. 270089), which is partially funded by the European Commission under the Seventh Framework program.

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  1. Department of Experimental Oncology, European Institute of Oncology, Milan, Italy

    Sebastiano de Franciscis & Alberto d’Onofrio

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  1. Sebastiano de Franciscis
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  2. Alberto d’Onofrio
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  1. Department of Experimental Oncology, European Institute of Oncology, Milan, Italy

    Alberto d'Onofrio

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de Franciscis, S., d’Onofrio, A. (2013). Spatiotemporal Bounded Noises and Their Application to the Ginzburg–Landau Equation. In: d'Onofrio, A. (eds) Bounded Noises in Physics, Biology, and Engineering. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7385-5_8

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