相关论文: Finding bifurcations in mathematical epidemiology …

Random graph models have been instrumental in characterizing complex networks, but chemical reaction networks (CRNs) are better represented as hypergraphs. Traditional models of random CRNs often reduce CRNs to bipartite graphs,…

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

The potential for multistationarity, or the existence of steady-state multiplicity, in the Earth System raises concerns that the planet could reach a climatic `tipping point,' rapidly transitioning to a warmer steady-state from which…

Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…

In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…

We describe combinatorial approaches to the question of whether families of real matrices admit pairs of nonreal eigenvalues passing through the imaginary axis. When the matrices arise as Jacobian matrices in the study of dynamical systems,…

The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness…

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…

In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…

Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…

The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and…

Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…

A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…

The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of…

Aspects of cell metabolism are modeled by ordinary differential equations describing the change of intracellular chemical concentrations. There is a correspondence between this dynamical system and a complex network. As in the classic…

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…

In this paper, we consider a general reaction-diffusion system with nonlocal effects and Neumann boundary conditions, where a spatial average kernel is chosen to be the nonlocal kernel. By virtue of the center manifold reduction technique…

Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…