CAO Huarong, WU Shiliang. Traveling Waves of a Delayed Differential System in a Lattice[J]. Applied Mathematics and Mechanics, 2018, 39(5): 592-610. doi: 10.21656/1000-0887.380165
Citation: CAO Huarong, WU Shiliang. Traveling Waves of a Delayed Differential System in a Lattice[J]. Applied Mathematics and Mechanics, 2018, 39(5): 592-610. doi: 10.21656/1000-0887.380165

Traveling Waves of a Delayed Differential System in a Lattice

doi: 10.21656/1000-0887.380165
  • Received Date: 2017-06-12
  • Rev Recd Date: 2017-09-06
  • Publish Date: 2018-05-15
  • The qualitative properties of traveling waves of a delayed differential system in a lattice with a quiescent stage were addressed. Under monostable and quasi-monotone assumptions, the existence of the traveling wave solutions were first established. Then, the asymptotic behavior, monotonicity and uniqueness of all wave profiles were proved. The exponential asymptotic stability of all non-critical traveling fronts was finally proved.
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