Related papers: Process-Oriented Geometric Singular Perturbation T…
We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study boundary data which are of staircase type and show rather…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
Blow-up in second and fourth order semi-linear parabolic partial differential equations (PDEs) is considered in bounded regions of one, two and three spatial dimensions with uniform initial data. A phenomenon whereby singularities form at…
Some ODE models treat ecological disturbance as a continuous process, even disturbances such as fire that occur almost instantaneously on the timescale of system recovery. Alternatively, flow-kick models resolve disturbances as discrete…
In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph…
Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
Simple conditions have been developed in [Zhang, Wahl and Yu, SIAM Rev. 2014; Yu and Wang, Math. Biosci. Eng. 2019], which are used to identify the existence of slow-fast relaxation oscillations that appear in differential systems, where…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
Optical Bloch Equations (OBEs) are canonical equations describing the dynamics of a classically driven atom coupled to a thermal bath. Their thermodynamics is highly relevant to establish fundamental energetic bounds of key quantum…
Time evolution of a perturbed thermal state is studied in a quantum-mechanical system with O(N) symmetry. In the limit of large N, time dependence of O(N)-singlet expectation values can be described by classical equations of motion in a…
The one-dimensional configuration coordinate model (1D-CCM) is widely used for the analysis of photoluminescence in molecules and doped solids, and relies on a linear combination of the equilibrium nuclear configurations of ground and…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
We explore quantum phase transitions using two probes of quantum chaos: out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the level spacing statistics. In particular, we address $p$-spin models associated with…