Article

# Travelling wavefronts of Belousov-Zhabotinskii system with diffusion and delay.

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China

Applied Mathematics Letters (Impact Factor: 1.5). 01/2009; 22:341-346. DOI: 10.1016/j.aml.2008.04.006 Source: DBLP

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**ABSTRACT:**This paper is concerned with a reaction–diffusion equation with time delay, which describes the dynamics of the blood cell production. The existence of the traveling wavefront is given by using the upper–lower solution technique and the monotone iteration.Applied Mathematics Letters 01/2010; · 1.50 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper is concerned with the travelling wavefronts of delayed lattice dynamical systems with global interaction. We establish the existence of the travelling wavefronts by upper–lower solutions technique and Schauder's fixed point theorem when the system satisfies the quasimonotone condition. The nonexistence of the travelling wavefronts of the system is considered by the comparison principle and the corresponding results of the scalar equation. Finally, we apply our main results to the Logistic model and Belousov–Zhabotinskii system on lattice. Our main finding here is that the global interaction can increase the minimal wave speed while the delay can decrease it.Journal of Difference Equations and Applications 12/2010; 16(12):1429-1446. · 0.74 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Existence of travelling wave front solution is established for diffusive and competitive Lotka–Volterra system with delays. The approach used in this paper is the upper-lower solution technique and the monotone iteration. The same results are suitable to Belousov–Zhabotinskii model with delays and cooperative Lotka–Volterra system with delays.Nonlinear Analysis Real World Applications 01/2010; 11(3):1323-1329. · 2.20 Impact Factor

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