Abstract
This work investigates the existence and non-existence of travelling wave solutions for Kolmogorov-type delayed lattice reaction-diffusion systems. Employing the cross iterative technique coupled with the explicit construction of upper and lower solutions in the theory of quasimonotone dynamical systems, we can find two threshold speeds c∗ and c∗ with c∗ c∗ >0. If the wave speed is greater than c∗, then we establish the existence of travelling wave solutions connecting two different equilibria. On the other hand, if the wave speed is smaller than c-∗, we further prove the non-existence result of travelling wave solutions. Finally, several ecological examples including one-species, two-species and three-species models with various functional responses and time delays are presented to illustrate the analytical results.
| Original language | English |
|---|---|
| Pages (from-to) | 1336-1367 |
| Number of pages | 32 |
| Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |
| Volume | 80 |
| Issue number | 5 |
| DOIs | |
| State | Published - 28 Oct 2014 |
Keywords
- Kolmogorov-type
- delayed lattice reaction-diffusion systems
- travelling wave solutions
- upper-lower solution