The diffusion-driven instability and complexity for a single-handed discrete Fisher equation
AffiliationUniversity of Chester; Tianjin University of Commerce
MetadataShow full item record
AbstractFor a reaction diffusion system, it is well known that the diffusion coefficient of the inhibitor must be bigger than that of the activator when the Turing instability is considered. However, the diffusion-driven instability/Turing instability for a single-handed discrete Fisher equation with the Neumann boundary conditions may occur and a series of 2-periodic patterns have been observed. Motivated by these pattern formations, the existence of 2-periodic solutions is established. Naturally, the periodic double and the chaos phenomenon should be considered. To this end, a simplest two elements system will be further discussed, the flip bifurcation theorem will be obtained by computing the center manifold, and the bifurcation diagrams will be simulated by using the shooting method. It proves that the Turing instability and the complexity of dynamical behaviors can be completely driven by the diffusion term. Additionally, those effective methods of numerical simulations are valid for experiments of other patterns, thus, are also beneficial for some application scientists.
CitationZhang, G., Zhang, R. and Yan, Y. (2020). The diffusion-driven instability and complexity for a single-handed discrete Fisher equation, Applied Mathematics and Computation, 371, 124946.
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0/