Related papers: Single--crossover recombination in discrete time
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened, or aggregated. As the neglected and unresolved terms become important, the utility of model predictions…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
A bilinearisation-reduction approach is described for finding solutions for nonlocal integrable systems and is illustrated with nonlocal discrete nonlinear Schr\"odinger equations. In this approach we first bilinearise the coupled system…
Physical nature of dimensional crossovers in weakly coupled Hubbard chains and ladders has been discussed within the framework of the perturbative renormalization-group approach. The difference between these two cases originates from…
This paper aims at providing rigorous numerical computation procedure for finite-time singularities in dynamical systems. Combination of time-scale desingularization as well as Lyapunov functions validation on stable manifolds of invariant…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
Cointegration is an important topic for time-series, and describes a relationship between two series in which a linear combination is stationary. Classically, the test for cointegration is based on a two stage process in which first the…
We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
For a general discrete dynamics on a Banach and Hilbert spaces we give a necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an exponential dichotomy on…
Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g., given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell's life…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer…
A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time…
The dynamics of a periodically driven system whose time evolution is governed by the Schr\"{o}dinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many…