The influence model
- 1 December 2001
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Control Systems
- Vol. 21 (6) , 52-64
- https://doi.org/10.1109/37.969135
Abstract
This article describes what we have termed the influence model, constructed to represent in a tractable way the dynamics of networked and interacting Markov chains. The constraints imposed on the influence model may restrict its modeling ability but permit explicit and detailed analysis and computation and still leave room for rather richly structured and novel behavior. We focus on the dynamic evolution of the system. The influence matrix H, in both the homogeneous and general cases, bears further study as an interesting generalization of familiar stochastic matrices. The influence model may also find use as a representation for stochastic signals of various kinds. The influence model is evidently related to other models of networked stochastic automata in the literature, but the details of the relationships remain to be worked out more explicitly in many cases. The generalizations embodied in the influence model could prove to be important degrees of freedom in particular applications.Keywords
This publication has 17 references indexed in Scilit:
- Exact results for one-dimensional cellular automata with different types of updatesPhysica A: Statistical Mechanics and its Applications, 1997
- Stochastic automata network of modeling parallel systemsIEEE Transactions on Software Engineering, 1991
- On the long term behavior of some finite particle systemsProbability Theory and Related Fields, 1990
- Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$The Annals of Probability, 1989
- Finite particle systems and infection modelsMathematical Proceedings of the Cambridge Philosophical Society, 1983
- An introduction to infinite particle systemsStochastic Processes and their Applications, 1981
- The basic contact processesStochastic Processes and their Applications, 1981
- Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter ModelThe Annals of Probability, 1975
- A model for spatial conflictBiometrika, 1973
- Time-Dependent Statistics of the Ising ModelJournal of Mathematical Physics, 1963