Propagation of monostable traveling fronts in discrete periodic media with delay

Shi Liang Wu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper is devoted to study the front propagation for a class of discrete periodic monostable equations with delay and nonlocal interaction. We first establish the existence of rightward and leftward spreading speeds and prove their coincidence with the minimal wave speeds of the pulsating traveling fronts in the right and left directions, respectively. The dependency of the speeds of propagation on the heterogeneity of the medium and the delay term is also investigated. We find that the periodicity of the medium increases the invasion speed, in comparison with a homogeneous medium; while the delay decreases the invasion speed. Further, we prove the uniqueness of all noncritical pulsating traveling fronts. Finally, we show that all noncritical pulsating traveling fronts are globally exponentially stable, as long as the initial perturbations around them are uniformly bounded in a weight space.

Original languageEnglish
Pages (from-to)2987-3022
Number of pages36
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number6
StatePublished - Jun 2018


  • Lattice periodic monostable equation
  • Pulsating traveling fronts
  • Spreading speed


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