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Nonlinear voter models: the transition from invasion to coexistence

Biomedical Sciences Research Institute Computer Science Research Institute Environmental Sciences Research Institute Nanotechnology & Advanced Materials Research Institute

Schweitzer, F and Behera, Laxmidhar (2009) Nonlinear voter models: the transition from invasion to coexistence. The European Physical Journal B, 67 (3). pp. 301-318. [Journal article]

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URL: http://www.springerlink.com/content/11301226n1244634/

DOI: 10.1140/epjb/e2009-00001-3

Abstract

In nonlinear voter models the transitions between two states depend in a nonlinear manneron the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to m = 4 neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicit expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion; (ii) random coexistence; and – most interestingly – (iii) correlated coexistence. These findings are contrasted with predictions fromthe mean-field phase diagram and are confirmed by extensive computer simulations of the microscopicdynamics.PACS. 87.23.Cc

Item Type:Journal article
Keywords:Population dynamics and ecological pattern formation, Dynamics of social systems
Faculties and Schools:Faculty of Computing & Engineering
Faculty of Computing & Engineering > School of Computing and Intelligent Systems
Research Institutes and Groups:Computer Science Research Institute
Computer Science Research Institute > Intelligent Systems Research Centre
ID Code:21058
Deposited By:Dr Laxmidhar Behera
Deposited On:13 Feb 2012 16:13
Last Modified:13 Feb 2012 16:13

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