### Abstract

Original language | English |
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Title of host publication | Bounded noises in physics, biology and engineering |

Editors | Alberto d'Onofrio |

Place of Publication | New York |

Publisher | Birkhäuser |

Pages | 151-168 |

Number of pages | 17 |

ISBN (Print) | 978-1-4614-7384-8 |

DOIs | |

Publication status | Published - 2013 |

### Publication series

Name | Modeling and Simulation in Science, Engineering and Technology |
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Publisher | Springer |

ISSN (Electronic) | 2164-3679 |

### Fingerprint

### Keywords

- bounded noises
- discrete-time dinamical systems
- random perturbations
- escape from attracting sets
- fractal dimension

### Cite this

*Bounded noises in physics, biology and engineering*(pp. 151-168). (Modeling and Simulation in Science, Engineering and Technology). New York: Birkhäuser. https://doi.org/10.1007/978-1-4614-7385-5_10

**Effects of bounded random perturbations on discrete dynamical systems.** / Rodrigues, Christian S.; de Moura, Alessandro P. S.; Grebogi, Celso.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Bounded noises in physics, biology and engineering.*Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, New York, pp. 151-168. https://doi.org/10.1007/978-1-4614-7385-5_10

}

TY - CHAP

T1 - Effects of bounded random perturbations on discrete dynamical systems

AU - Rodrigues, Christian S.

AU - de Moura, Alessandro P. S.

AU - Grebogi, Celso

PY - 2013

Y1 - 2013

N2 - In this chapter we discuss random perturbations and their effect on dynamical systems. We focus on discrete time dynamics and present different ways of implementing the random dynamics, namely the dynamics of random uncorrelated noise and the dynamics of random maps. We discuss some applications in scattering and in escaping from attracting sets. As we shall see, the perturbations may dramatically change the asymptotic behaviour of these systems. In particular, in randomly perturbed non-hyperbolic scattering trajectories may escape from regions where otherwise they are expected to be trapped forever. The dynamics also gains hyperbolic-like characteristics. These are observed in the decay of survival probability as well as in the fractal dimension of singular sets. In addition, we show that random perturbations also trigger escape from attracting sets, giving rise to transport among basins. Along the chapter, we motivate the application of such processes. We finish by suggesting some possible further applications.

AB - In this chapter we discuss random perturbations and their effect on dynamical systems. We focus on discrete time dynamics and present different ways of implementing the random dynamics, namely the dynamics of random uncorrelated noise and the dynamics of random maps. We discuss some applications in scattering and in escaping from attracting sets. As we shall see, the perturbations may dramatically change the asymptotic behaviour of these systems. In particular, in randomly perturbed non-hyperbolic scattering trajectories may escape from regions where otherwise they are expected to be trapped forever. The dynamics also gains hyperbolic-like characteristics. These are observed in the decay of survival probability as well as in the fractal dimension of singular sets. In addition, we show that random perturbations also trigger escape from attracting sets, giving rise to transport among basins. Along the chapter, we motivate the application of such processes. We finish by suggesting some possible further applications.

KW - bounded noises

KW - discrete-time dinamical systems

KW - random perturbations

KW - escape from attracting sets

KW - fractal dimension

U2 - 10.1007/978-1-4614-7385-5_10

DO - 10.1007/978-1-4614-7385-5_10

M3 - Chapter

SN - 978-1-4614-7384-8

T3 - Modeling and Simulation in Science, Engineering and Technology

SP - 151

EP - 168

BT - Bounded noises in physics, biology and engineering

A2 - d'Onofrio, Alberto

PB - Birkhäuser

CY - New York

ER -