Markovian Switching of Mutation Rates in Evolutionary Network Dynamics

@article{Vlasic2021MarkovianSO,
  title={Markovian Switching of Mutation Rates in Evolutionary Network Dynamics},
  author={Andrew Vlasic},
  journal={IGTR},
  year={2021},
  volume={23},
  pages={2150001:1-2150001:18}
}
The replicator–mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent networks. For the two type population, a bifurcation point of the mutation rate was derived, displaying different long-run behaviors above and below this point. The long-run behavior would naturally be subjected to noise from the environment, however, to date… 

Figures from this paper

References

SHOWING 1-10 OF 26 REFERENCES

Limit cycles in replicator-mutator network dynamics

TLDR
Asymmetry in fitness is explored and it is shown that the replicator-mutator equations exhibit Hopf bifurcations and limit cycles, which correspond to sustained oscillations in decisions across the group.

Hopf Bifurcations and Limit Cycles in Evolutionary Network Dynamics

TLDR
Asymmetry in fitness is explored and it is shown that the replicator-mutator equations exhibit Hopf bifurcations and limit cycles, which correspond to oscillations of grammar dominance in language evolution and to oscillation in behavioral preferences in social networks.

Stochastic Replicator Dynamics Subject to Markovian Switching

Evolutionary Games and Population Dynamics

TLDR
In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.

The SIS epidemic model with Markovian switching

Evolutionary dynamics of behavior in social networks

  • R. Olfati-Saber
  • Computer Science
    2007 46th IEEE Conference on Decision and Control
  • 2007
TLDR
This paper defines the notion of "behavior networks" and introduces a novel social choice model (i.e. mutation model) for evolutionary dynamics of behavior in social networks that exhibits a rich set of emergent phases of evolution.

On Equilibrium Properties of the Replicator-Mutator Equation in Deterministic and Random Games

TLDR
It is observed that introducing mutation results in a larger average number of internal equilibria than when mutation is absent, implying that mutation leads to larger behavioural diversity in dynamical systems.

Regularity and Recurrence of Switching Diffusions

This work is concerned with switching diffusion processes, also known as regime-switching diffusions. Our attention focuses on regularity, recurrence, and positive recurrence of the underlying

Exponential and Uniform Ergodicity of Markov Processes

General characterizations of geometric convergence for Markov chains in discrete time on a general state space have been developed recently in considerable detail. Here we develop a similar theory

Continuous-Time Markov Chains

Continuous time Markov chains have steady state probability solutions if and only if they are ergodic, just like discrete time Markov chains. Finding the steady state probability vector for a