Related papers: A numerical framework for computing steady states …
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics,…
In this paper, we have emphasized the stability analysis of the accelerating cosmological models obtained in $f(T)$ gravity theory. The behavior of the models based on the evolution of the equation of state parameter shows phantom-like…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
In this paper, we present a numerical analysis of the hydrostatic Stokes equations, which are linearization of the primitive equations describing the geophysical flows of the ocean and the atmosphere. The hydrostatic Stokes equations can be…
Repeated small dynamic networks are integral to studies in evolutionary game theory, where networked public goods games offer novel insights into human behaviors. Building on these findings, it is necessary to develop a statistical model…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
We report how strategic evolution can stabilize topological states in a network of FitzHugh-Nagumo systems. The evolution follows a repeated process of adding or deleting of links between two nodes that is decided based on a threshold set…
This paper studies the steady-states to a diffusive Lotka-Volterra cooperative model with population flux by attractive transition. The first result gives many bifurcation points on the branch of the positive constant solution under the…
This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces. The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the $p$th-mean…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
We investigate numerical solution of $Q^2$ evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method.…
The Shigesada-Kawasaki-Teramoto (SKT) model has become a classical modelling framework for studying spatial segregation and cross-diffusion-driven pattern formation in competing populations. This model assumes phenotypic homogeneity, but…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
We consider a continuum phase field model for crystal growth via molecular beam epitaxy, with the goal of determining stable numerical time integration methods for the dynamics. We parametrize a class of semi-implicit methods that are…
Established populations often exhibit oscillations in their sizes. If a population is isolated, intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a…