ABSTRACT: The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior. Then, by employing
the comparison principle and upper and lower solutions technique, we prove the asymptotic stability and uniqueness of such
monostable wavefronts in the sense of phase shift and circumnutation. We also obtain some similar results in ℝ.
Keywordsdiscrete-time integral recursion-comparison principle-upper and lower solutions-monostable wave-stability
Science China Mathematics 04/2012; 53(5):1185-1194. · 0.33 Impact Factor