Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Gentz, Barbara"'
Publikováno v:
Journal of Dynamics and Differential Equations, Vol. 27, No. 1, pp. 83-136, 2015
We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be described by a
Externí odkaz:
http://arxiv.org/abs/1312.6353
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
SIAM J. Math. Anal., 46(1):310-352 (2014)
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first ex
Externí odkaz:
http://arxiv.org/abs/1208.2557
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
Electronic J. Probability 18 (2013), no 24, 1-58
We prove a Kramers-type law for metastable transition times for a class of one-dimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the potential energy
Externí odkaz:
http://arxiv.org/abs/1202.0990
Publikováno v:
J. Differential Equations 252 (2012) 4786-4841
We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting
Externí odkaz:
http://arxiv.org/abs/1011.3193
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
Journal of Physics A Mathematical and Theoretical 42, 5 (2009) 052001
We consider a Ginzburg-Landau partial differential equation in a bounded interval, perturbed by weak spatio-temporal noise. As the interval length increases, a transition between activation regimes occurs, in which the classical Kramers rate diverges
Externí odkaz:
http://arxiv.org/abs/0809.2652
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
Markov Processes and Related Fields 16, 3 (2010) 549?598
The Eyring-Kramers law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. In the weak-noise limit, the transition time is to leading order exponential in the potential difference to ov
Externí odkaz:
http://arxiv.org/abs/0807.1681
Publikováno v:
Nonlinearity 20, 11 (2007) 2583-2614
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to a
Externí odkaz:
http://arxiv.org/abs/math/0611648
Publikováno v:
Nonlinearity 20, 11 (2007) 2551-2581
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of w
Externí odkaz:
http://arxiv.org/abs/math/0611647
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
Europhys. Letters 70:1-7 (2005)
We present mathematically rigorous expressions for the residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions
Externí odkaz:
http://arxiv.org/abs/cond-mat/0408321
Autor:
Berglund, Nils, Gentz, Barbara
Publikováno v:
J. Statist. Phys. 114:1577-1618 (2004)
We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips between sy
Externí odkaz:
http://arxiv.org/abs/math/0308175