Volume 125, Number 2, January 2019
|Number of page(s)||6|
|Published online||12 February 2019|
Identifying dynamical structures in the physical space of stochastic processes
1 Departamento de Física, Universidade Federal do Paraná - 81531-980, Curitiba-PR, Brazil
2 Departamento de Física and National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte - 59078-970, Natal- RN, Brazil
3 Departamento de Física, Universidade do Estado de Santa Catarina - 89219-710, Joinville-SC, Brazil
4 Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco 50670-901, Recife-PE, Brazil
5 Physics Department, Clarkson University - Potsdam, NY 13699-5820, USA
Received: 19 October 2018
Accepted: 11 January 2019
Characterizing dynamical patterns in the (physical) state space of stochastic processes can be a challenging task. From two visualization techniques, the observable-representation and k-means clustering, a unified framework to identify such structures is developed. The only information required is the system transition matrix R (a quantity that can be directly accessed from experimental data). The approach is illustrated through the analysis of random searches for targets distributed in patchy environments. The protocol —for R constructed from a typical tracked long trajectory— is able to reveal the shape and locations of all the landscape patches. The method constitutes a valuable new tool to study the underlying geometry of general stochastic processes.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.Tp – Time series analysis
© EPLA, 2019
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