Existence of traveling wave solutions in \(m\)-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction
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Authors
Kai Zhou
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China.
- School of Mathematics and Computer, Chizhou University, Chizhou 247000, P. R. China.
Abstract
This paper deals with the existence of traveling wave solutions for \(m\)-dimensional delayed lattice dynamical systems with
competitive quasimonotone and global interaction. By using Schauder’s fixed point theorem and a cross-iteration scheme, we
reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results
obtained will be applied to \(m\)-dimensional delayed lattice dynamical systems with Lotka-Volterra type competitive reaction
terms and global interaction.
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ISRP Style
Kai Zhou, Existence of traveling wave solutions in \(m\)-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3630--3642
AMA Style
Zhou Kai, Existence of traveling wave solutions in \(m\)-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction. J. Nonlinear Sci. Appl. (2017); 10(7):3630--3642
Chicago/Turabian Style
Zhou, Kai. "Existence of traveling wave solutions in \(m\)-dimensional delayed lattice dynamical systems with competitive quasimonotone and global interaction." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3630--3642
Keywords
- Traveling wave solutions
- lattice differential systems
- delay
- upper and lower solutions
- Schauder’s fixed point theorem.
MSC
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