Displaying similar documents to “Traveling wave solutions in a class of higher dimensional lattice differential systems with delays and applications”

Propagation of delayed lattice differential equations without local quasimonotonicity

Shuxia Pan (2015)

Annales Polonici Mathematici

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This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by investigating the existence and nonexistence of traveling wave solutions.

The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

Igor Sazonov, Mark Kelbert, Michael B. Gravenor (2008)

Mathematical Modelling of Natural Phenomena

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A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is considered numerically and analytically. The limiting solutions describing the behaviour of the standard SIR model with a small number of initially infected individuals are derived, and expressions found for the duration of an outbreak. We study a model for a weakly mixed population distributed between the interacting centres. The centres are modelled as SIR nodes with interaction between sites determined...

Uniqueness of Monotone Mono-stable Waves for Reaction-Diffusion Equations with Time Delay

W. Huang, M. Han, M. Puckett (2009)

Mathematical Modelling of Natural Phenomena

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Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some competition systems. However, the problem on the uniqueness of traveling wave (for a fixed...

Waves of excitations in heterogeneous annular region II. Strong asymmetry

Kristóf Kály-Kullai, András Volford, Henrik Farkas (2003)

Banach Center Publications

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Excitation wave propagation in a heterogeneous medium around a circular obstacle is investigated, when the obstacle is located very eccentrically with respect to the interfacial circle separating the slow inner and the fast outer region. Qualitative properties of the permanent wave fronts are described, and the calculated wave forms are presented.