Spatiotemporal patterns in coupled reaction-diffusion systems with nonidentical kinetics

被引:0
作者
Fan, Wei-li [1 ]
Deng, Teng-kun [1 ]
Liu, Shuang [1 ]
Liu, Ruo-qi [1 ]
He, Ya-feng [1 ,2 ]
Liu, Ya-hui [1 ]
Liu, Yi-ning [1 ]
Liu, Fu-cheng [1 ,3 ]
机构
[1] Hebei Univ, Coll Phys Sci & Technol, Baoding 071002, Peoples R China
[2] Hebei Univ, Inst Environm Engn, Baoding 071002, Peoples R China
[3] Hebei Univ, Inst Life Sci & Green Dev, Baoding 071002, Peoples R China
基金
中国国家自然科学基金;
关键词
TURING PATTERNS;
D O I
10.1103/PhysRevE.111.024210
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Understanding of the effect of coupling interaction is at the heart of nonlinear science since some nonequilibrium systems are composed of different layers or units. In this paper, we demonstrate various spatio-temporal patterns in a nonlinearly coupled two-layer Turing system with nonidentical reaction kinetics. Both the type of Turing mode and coupling form play an important role in the pattern formation and pattern selection. Two kinds of Turing mode interactions, namely supercritical-subcritical and supercritical-supercritical Turing mode interaction, have been investigated. Stationary resonant superlattice patterns arise spontaneously in both cases, while dynamic patterns can also be formed in the latter case. The destabilization of spike solutions induced by spatial heterogeneity may be responsible for these dynamic patterns. In contrast to linear coupling, the nonlinear coupling not only increases the complexity of spatio-temporal patterns, but also reduces the requirements of spatial resonance conditions. The simulation results are in good agreement with the experimental observations in dielectric barrier discharge systems.
引用
收藏
页数:8
相关论文
共 59 条
[1]   Nonlinear effects on Turing patterns: Time oscillations and chaos [J].
Aragon, J. L. ;
Barrio, R. A. ;
Woolley, T. E. ;
Baker, R. E. ;
Maini, P. K. .
PHYSICAL REVIEW E, 2012, 86 (02)
[2]   Turing patterns in multiplex networks [J].
Asllani, Malbor ;
Busiello, Daniel M. ;
Carletti, Timoteo ;
Fanelli, Duccio ;
Planchon, Gwendoline .
PHYSICAL REVIEW E, 2014, 90 (04)
[3]   A two-dimensional numerical study of spatial pattern formation in interacting Turing systems [J].
Barrio, RA ;
Varea, C ;
Aragón, JL ;
Maini, PK .
BULLETIN OF MATHEMATICAL BIOLOGY, 1999, 61 (03) :483-505
[4]   Modeling the skin pattern of fishes [J].
Barrio, Rafael A. ;
Baker, Ruth E. ;
Vaughan, Benjamin, Jr. ;
Tribuzy, Karla ;
de Carvalho, Marcelo R. ;
Bassanezi, Rodney ;
Maini, Philip K. .
PHYSICAL REVIEW E, 2009, 79 (03)
[5]  
Berenstein I, 2004, PHYS REV E, V70, DOI 10.1103/PhysRevE.70.046219
[6]   Generation, annihilation, dynamics and self-organized patterns of filaments in dielectric barrier discharge plasmas [J].
Boeuf, J. P. ;
Bernecker, B. ;
Callegari, Th ;
Blanco, S. ;
Fournier, R. .
APPLIED PHYSICS LETTERS, 2012, 100 (24)
[7]   Master stability functions reveal diffusion-driven pattern formation in networks [J].
Brechtel, Andreas ;
Gramlich, Philipp ;
Ritterskamp, Daniel ;
Drossel, Barbara ;
Gross, Thilo .
PHYSICAL REVIEW E, 2018, 97 (03)
[8]   Pattern formation and dynamics of plasma filaments in dielectric barrier discharges [J].
Callegari, T. ;
Bernecker, B. ;
Boeuf, J. P. .
PLASMA SOURCES SCIENCE & TECHNOLOGY, 2014, 23 (05)
[9]   Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems [J].
Castelino, Jennifer K. ;
Ratliff, Daniel J. ;
Rucklidge, Alastair M. ;
Subramanian, Priya ;
Topaz, Chad M. .
PHYSICA D-NONLINEAR PHENOMENA, 2020, 409
[10]   Instabilities and patterns in coupled reaction-diffusion layers [J].
Catlla, Anne J. ;
McNamara, Amelia ;
Topaz, Chad M. .
PHYSICAL REVIEW E, 2012, 85 (02)