相关论文: From Discrete to Continuous Highest-earning Imitat…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…
Imitation is widely observed in populations of decision-making agents. Using our recent convergence results for asynchronous imitation dynamics on networks, we consider how such networks can be efficiently driven to a desired equilibrium…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in…
In this letter we present a stochastic dynamic model which can explain economic cycles. We show that the macroscopic description yields a complex dynamical landscape consisting of multiple stable fixed points, each corresponding to a split…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…