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Identifying stochastic basin hopping by partitioning with graph modularity

Santitissadeekorn, N and Bollt, EM (2007) Identifying stochastic basin hopping by partitioning with graph modularity Physica D: Nonlinear Phenomena, 231 (2). pp. 95-107.

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Abstract

It has been known that noise in a stochastically perturbed dynamical system can destroy what was the original zero-noise case barriers in the phase space (pseudobarrier). Noise can cause the basin hopping. We use the Frobenius-Perron operator and its finite rank approximation by the Ulam-Galerkin method to study transport mechanism of a noisy map. In order to identify the regions of high transport activity in the phase space and to determine flux across the pseudobarriers, we adapt a new graph theoretical method which was developed to detect active pseudobarriers in the original phase space of the stochastic dynamic. Previous methods to identify basins and basin barriers require a priori knowledge of a mathematical model of the system, and hence cannot be applied to observed time series data of which a mathematical model is not known. Here we describe a novel graph method based on optimization of the modularity measure of a network and introduce its application for determining pseudobarriers in the phase space of a multi-stable system only known through observed data. © 2007 Elsevier Ltd. All rights reserved.

Item Type: Article
Authors :
NameEmailORCID
Santitissadeekorn, Nn.santitissadeekorn@surrey.ac.ukUNSPECIFIED
Bollt, EMUNSPECIFIEDUNSPECIFIED
Date : 15 July 2007
Identification Number : 10.1016/j.physd.2007.04.008
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:21
Last Modified : 17 May 2017 15:10
URI: http://epubs.surrey.ac.uk/id/eprint/838865

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