Abstract
This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n,t) ×. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In particular, it is shown that the traveling wave fronts are on the boundary of the manifold. Furthermore, uniqueness and stability of such entire solutions are studied.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 78-103 |
| Number of pages | 26 |
| Journal | Mathematical Modelling of Natural Phenomena |
| Volume | 8 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2013 |
Fingerprint
Keywords
- Bistable nonlinearity
- Entire solution
- Lattice delayed differential equation
- Traveling wave front
ASJC Scopus subject areas
- Modeling and Simulation
Cite this
Entire solutions in lattice delayed differential equations with nonlocal interaction : Bistable cases. / Wang, Z. C.; Li, W. T.; Ruan, Shigui.
In: Mathematical Modelling of Natural Phenomena, Vol. 8, No. 3, 2013, p. 78-103.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Entire solutions in lattice delayed differential equations with nonlocal interaction
T2 - Bistable cases
AU - Wang, Z. C.
AU - Li, W. T.
AU - Ruan, Shigui
PY - 2013
Y1 - 2013
N2 - This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n,t) ×. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In particular, it is shown that the traveling wave fronts are on the boundary of the manifold. Furthermore, uniqueness and stability of such entire solutions are studied.
AB - This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n,t) ×. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In particular, it is shown that the traveling wave fronts are on the boundary of the manifold. Furthermore, uniqueness and stability of such entire solutions are studied.
KW - Bistable nonlinearity
KW - Entire solution
KW - Lattice delayed differential equation
KW - Traveling wave front
UR - http://www.scopus.com/inward/record.url?scp=84879314113&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879314113&partnerID=8YFLogxK
U2 - 10.1051/mmnp/20138307
DO - 10.1051/mmnp/20138307
M3 - Article
AN - SCOPUS:84879314113
VL - 8
SP - 78
EP - 103
JO - Mathematical Modelling of Natural Phenomena
JF - Mathematical Modelling of Natural Phenomena
SN - 0973-5348
IS - 3
ER -