Journal
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
Volume 529, Issue 2, Pages 199-264Publisher
ELSEVIER
DOI: 10.1016/j.physrep.2013.03.004
Keywords
Complex networks; Markovian dynamics; Master equation; Stochastic nonlinear dynamics; Potential energy landscape; Thermodynamic analysis
Categories
Funding
- DoD High Performance Computing Modernization Program through the National Defense Science and Engineering Graduate (NDSEG) Fellowship [32 CFR 168a]
- National Science Foundation (NSF) [CCF-0849907, CCF-1217213]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1217213] Funding Source: National Science Foundation
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Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples. (C) 2013 Elsevier B.V. All rights reserved.
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