Turing patterns of Gierer–Meinhardt model on complex networks

• Published in: Nonlinear dynamics Vol. 105; no. 1; pp. 899 - 909
• Main Authors: Guo, Luyao, Shi, Xinli, Cao, Jinde
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-07-2021; Springer Nature B.V
• Subjects: Automotive Engineering; Biological models (mathematics); Classical Mechanics; Control; Dynamical Systems; Engineering; Formations; Influence; Mechanical Engineering; Network topologies; Numerical analysis; Partial differential equations; Review; Vibration; Reaction diffusion; Exponential decay; Gierer-Meinhardt model; Complex network; Turing pattern
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06618-6

Gierer–Meinhardt (G–M) model is a classical reaction diffusion (RD) model to describe biological and chemical phenomena. Turing patterns of G–M model in continuous space have attracted much attention of researchers. Considering that the RD system defined on discrete network structure is more practical in many aspects than the corresponding system in continuous space, we study Turing patterns of G–M model on complex networks. By numerical simulations, Turing patterns of the G–M model on regular lattice networks and several complex networks are studied, and the influences of system parameters, network types and average degree on pattern formations are discussed. Furthermore, we present an exponential decay of Turing patterns on complex networks, which not only quantitatively depicts the influence of network topology on pattern formations, but also provides the possibility for predict pattern formations.