 Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domainsDaifeng Duan, Biao Liu and Junjie Wei Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 366-383 Abstract: We investigate the effects of periodic boundary conditions on a nonlocal Holling–Tanner model defined on a square domain. A top-hat kernel function with finite support is employed to characterize nonlocal interactions, which we further adapt to accommodate periodic boundary conditions. Subsequently, we derive the Turing and spatiotemporal Hopf bifurcation curves and conduct numerical simulations across the parameter ranges delineated by these curves. Our findings demonstrate substantial differences in spatiotemporal patterns between the square domain and the one-dimensional case, including squares, stripes, mixed states, irregular spot-like hexagonal patterns, and coexistence states of three-stripes and spots. These observed patterns exhibit remarkable consistency with both chemical experimental results and the skin pigmentation patterns of fish, thereby offering valuable theoretical insights and predictive frameworks for understanding spatiotemporal patterns in chemical and biological systems. Keywords: Square domain; Top-hat kernel function; Holling–Tanner model; Periodic boundary condition; Spatiotemporal Hopf bifurcation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:366-383 DOI: 10.1016/j.matcom.2026.01.025 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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