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We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
Analytical approaches in models of opinion formation have been extensively studied either for an opinion represented as a discrete or a continuous variable. In this paper, we analyze a model which combines both approaches. The state of an…
State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that…
In this work, we are motivated by a recent variant of the nonlinear Schrodinger (NLS) equation describing cold, dilute atomic condensates with quantum fluctuation effects. Our goal is to develop robust numerical methods capable of…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
We focus at the interface between multiscale computations, bifurcation theory and social networks. In particular we address how the Equation-Free approach, a recently developed computational framework, can be exploited to systematically…
In this paper, we study the numerical solutions of the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations…
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We…
This paper addresses the stabilization problem of stochastic jump systems (SJSs) closed by a generally sampled controller. Because of the controller's switching and state both sampled, it is challenging to study its stabilization. A new…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
We investigate network of degenerate optical parametric oscillators (DOPOs) as a model of the coherent Ising machine, an architecture for solving Ising problems. The network represents the interaction in the Ising model, which is a…
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…