title: Traveling wave governs the stability of spatial pattern in a model of allelopathic competition interactions.
abstract: Inhomogenous distribution of populations across physical space is a widely observed scenario in nature and has been studied extensively. Mechanisms accounting for these observations are such as diffusion-driven instability and mechanochemical approach. While conditions have been derived from a variety of models in biological, physical, and chemical systems to trigger the emergence of spatial patterns, it remains poorly understood whether the spatial pattern possesses asymptotical stability. In a plankton allelopathic competitive system with distributed time delay, we found that spatial pattern arises as a result of Hopf bifurcation and, in the meantime, there exists a unique asymptotically stable traveling wave solution. The convergence of the traveling wave solution to the emergent pattern and its stability infer that the emergent spatial pattern is locally asymptotically stable.
authors.affiliation: Department of Basic Sciences, Yancheng Institute of Technology, Yancheng 224003, China.
authors.forename: Canrong
authors.initials: C
authors.lastname: Tian
authors.forename: Lai
authors.initials: L
authors.lastname: Zhang