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Dynamical Systems Driven by Dichotomous Noise

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Bounded Noises in Physics, Biology, and Engineering

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Abstract

Dichotomous Markov noise is a two-state bounded stochastic process. Its simple structure allows exact solutions of steady-state probability density function to be obtained analytically in one-dimensional differential models. It is used to describe the random switching between two deterministic dynamics and to investigate the effect of the noise correlation. This chapter describes the fundamental properties of the dichotomous noise and the main analytical results about one-dimensional stochastic differential equations forced by additive and multiplicative dichotomous noise. Noise-induced transitions (i.e., structural changes of the system behavior) in systems driven by such type of noise are also recalled; finally, some emblematic examples of use of dichotomous noise in the environmental sciences are described.

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Authors and Affiliations

  1. DIATI, Politecnico di Torino, Turin, Italy

    Luca Ridolfi & Francesco Laio

Authors
  1. Luca Ridolfi
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  2. Francesco Laio
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Correspondence to Luca Ridolfi .

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Editors and Affiliations

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

    Alberto d'Onofrio

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Ridolfi, L., Laio, F. (2013). Dynamical Systems Driven by Dichotomous Noise. 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_4

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