Stochastic Traveling Wave Solution to a Stochastic KPP EquationSpringer Science and Business Media LLC - Tập 28 - Trang 389-417 - 2015
Zhehao Huang, Zhengrong Liu, Zhenzhen Wang
In this paper, we consider the stochastic KPP equation which is perturbed by an environmental noise. Applying an extended stochastic ordering technique, we establish the existence of a stochastic traveling wave solution to the equation and give a sufficient condition under which solutions can be attracted to the stochastic traveling wave.
Spatial Propagation for an Epidemic Model in a Patchy EnvironmentSpringer Science and Business Media LLC - - Trang 1-25 - 2023
Zhaoquan Xu, Tianwei Tan, Cheng-Hsiung Hsu
This paper investigates the propagation dynamics for an epidemic model with nonlinear incidence rates in a patchy environment. Giving a general setting of the nonlinear incidence rates (monotone or non-monotone), we establish a framework that provides a complete characterization on the existence, non-existence and minimal wave speed of traveling waves which describe the evolution of disease starti...... hiện toàn bộ
Heteroclinic orbits in singular systems: A unifying approachSpringer Science and Business Media LLC - Tập 6 - Trang 147-173 - 1994
Flaviano Battelli
We consider singularly perturbed systems
$$\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )$$
, such thatξ=f(ξ, αo, 0). αo∃ℝ
m
, has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system ha...... hiện toàn bộ
On a Differential Equation with State-Dependent DelaySpringer Science and Business Media LLC - Tập 24 - Trang 197-248 - 2012
Eugen Stumpf
We study a family of scalar differential equations with a single parameter a > 0 and delay r > 0. In the case of the constant delay r = 1 it is known that for parameters 0 < a < 1 the trivial solution of this family is asymptotically stable, whereas for a > 1 the trivial solution gets unstable, and a global center-unstable manifold connects the trivial solution to a slowly oscillating periodic orb...... hiện toàn bộ
Comparison between the Deterministic and Stochastic Models of Nonlocal DiffusionSpringer Science and Business Media LLC - - Trang 1-20 - 2022
Itsuki Watanabe, Hiroshi Toyoizumi
In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference ...... hiện toàn bộ
Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin GasdynamicsSpringer Science and Business Media LLC - Tập 34 - Trang 1067-1084 - 2020
Rahul Kumar Chaturvedi, L. P. Singh, Dia Zeidan
The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine–Hugoniot relations for delta shock wave which are utilized to determine the strength, posi...... hiện toàn bộ
Dynamical Properties of Models for the Calvin CycleSpringer Science and Business Media LLC - Tập 26 - Trang 673-705 - 2014
Alan D. Rendall, Juan J. L. Velázquez
Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric coefficients and chemical kinetics and whether or not diffusion is taken into account. This paper studies the long-time behaviour of solutions of several of th...... hiện toàn bộ