Related papers: Random evolution equations: well-posedness, asympt…
An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
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 compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
The work deals with a study of a nonlinear parabolic equation with hysteresis, containing a nonlinear monotone operator in the diffusion term. The well-posedness of the model equation is addressed by using an implicit time discretization…
Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for…
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a…
We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…
In this paper we consider a class of non-local in time telegraph equations. Recently, it has been proved that the fundamental solutions of such equations can be interpreted as the probability density function of a stochastic process. We…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…