Stochastic Spatial Models: A Hyper-Tutorial
A. Basic Definitions
- Notation, lattices, and neighbors
- Continuous time Markov chains
- Distributions, Stationarity
- Coexistence and Related Concepts
B. Genetics: Voter Models
- Coexistence or Consensus?
- One Dimension
- Coalescing Random Walks
- Hybrid zones: Inferior Heterozygotes
C. Growth Models
- Richardson's model
- Biased voter model
- Contact process
- Long Range Limits
- Quadratic birth rates
- Rapid Stirring Limits
- Nonlinear voter model
Multitype Models (The Big Picture)
D. Case 1. Attracting Fixed Point
- Grass-bushes-trees
- Competition of species
- Predator-prey system
- Predator-mediated coexistence
E. Case 2. Bistability
- Competing contact processes
- Colicin
- Catalyst Surface
F. Case 3. Cyclic Systems
- Epidemic models
- Multitype biased voter model
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- Nonlinear predator-prey system
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