Work

Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction–diffusion model

Year: 2016

Type: article

Abstract: The Fisher–Rao metric from information geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of information geometry to study more general phase transitions in complex systems. However, it is unclear whether the Fisher–Rao metric does indeed detect these more general transitions, especially in the absence of a statistical model. In this paper we study the transitions between patterns in the Gray-Scott reaction–diffusion model using Fisher information. We describe the system by a probability density function that represents the size distribution of blobs in the patterns and compute its Fisher information with respect to changing the two rate parameters of the underlying model. We estimate the distribution non-parametrically so that we do not assume any statistical model. The resulting Fisher map can be interpreted as a phase-map of the different patterns. Lines with high Fisher information can be considered as boundaries between regions of parameter space where patterns with similar characteristics appear. These lines of high Fisher information can be interpreted as phase transitions between complex patterns.

Source: Journal of Statistical Mechanics Theory and Experiment

DOI: 10.1088/1742-5468/2016/04/043301

Authors: Omri Har-Shemesh, Rick Quax, Alfons G Hoekstra, Peter M A Sloot

Institutions: University of Amsterdam, ITMO University, Nanyang Technological University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: European Commission