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Oscillatory dynamics in rock–paper–scissors games with mutations
- Publication Year :
- 2010
- Publisher :
- Elsevier, 2010.
-
Abstract
- We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude.<br />Comment: 25 pages, 9 figures. To appear in the Journal of Theoretical Biology
- Subjects :
- Mutation rate
Population Dynamics
Fixed point
Parameter space
01 natural sciences
010305 fluids & plasmas
Quantitative Biology::Populations and Evolution
Statistical physics
Limit (mathematics)
Mathematics
Reproduction
Applied Mathematics
Biodiversity
General Medicine
Biological Evolution
Nonlinear Sciences - Adaptation and Self-Organizing Systems
Markov Chains
Amplitude
Modeling and Simulation
symbols
General Agricultural and Biological Sciences
Adaptation and Self-Organizing Systems (nlin.AO)
Algorithms
Statistics and Probability
Physics - Physics and Society
FOS: Physical sciences
Physics and Society (physics.soc-ph)
Models, Biological
General Biochemistry, Genetics and Molecular Biology
symbols.namesake
Game Theory
Control theory
Limit cycle
0103 physical sciences
Computer Simulation
Selection, Genetic
Quantitative Biology - Populations and Evolution
010306 general physics
Condensed Matter - Statistical Mechanics
Ecosystem
Hopf bifurcation
Stochastic Processes
General Immunology and Microbiology
Statistical Mechanics (cond-mat.stat-mech)
Stochastic process
Populations and Evolution (q-bio.PE)
Kinetics
Nonlinear Dynamics
FOS: Biological sciences
Mutation
Linear Models
Subjects
Details
- Language :
- English
- ISSN :
- 00225193
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....95e20b0a8673c2a235ef72ba9bc6e30a