Related papers: A note on the replicator equation with explicit sp…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…
This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…
We consider robust output regulation of a partial differential equation model describing temperature evolution in a room. More precisely, we examine a two-dimensional room model with the velocity field and temperature evolution governed by…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
In this paper we establish local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…
We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
We consider one dimensional isentropic compressible Navier-Stokes equations with Oldroyd-type constitutive law. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with…
We discuss how to use a Genetic Regulatory Network as an evolutionary representation to solve a typical GP reinforcement problem, the pole balancing. The network is a modified version of an Artificial Regulatory Network proposed a few years…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$\Delta$) $\alpha$/2 in the diffusion term. In the…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…
We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically…