Delay-driven spatial patterns in a plankton allelopathic system

Spatial patterns have received considerable attention in the physical, biological, and social sciences. Generally speaking, time delay is a prevailing phenomenon in aquatic environments, since the production of allelopathic substance by competitive species is not instantaneous, but mediated by some time lag required for maturity of species. A natural question is how delay affects the spatial patterns. Here, we consider a delayed plankton allelopathic system consisting of two competitive species and analytically investigate how the time delay affects the stability and spatial patterns. Based upon a stability analysis, we demonstrate that the delay can induce spatial patterns under some conditions. Moreover, by use of a series of numerical simulations performed with a finite difference scheme, we show that the delay plays an important role on pattern selection. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3692963]