Related papers: Metastability in Stochastic Replicator Dynamics
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…
We investigate the impact of payoff shocks on the evolution of large populations of myopic players that employ simple strategy revision protocols such as the "imitation of success". In the noiseless case, this process is governed by the…
We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
The conventional Langevin equation offers a mathematically convenient framework for investigating open stochastic systems interacting with their environment or a bath. However, it is not suitable for a wide variety of systems whose dynamics…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
Metastability appears when a thermodynamic system, such as supercooled water (which is liquid below freezing temperature), lands on the "wrong" side of a phase transition, and remains for a very long time in a state different from its…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…
Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…