Effect of subdiffusion on the dynamics of pattern formation is studied near codimension-two Turing-Hopf bifurcations in a fractional-in-time Oregonator model.Stability analysis is performed by using Fourier and Laplace transforms,and numerical simulations are conducted in one dimension.Our results have shown that the subdiffusion of activator can depress Turing mode and promote Hopf mode.In the case of subdiffusion of inhibitor,the results are reversed.The results obtained here are helpful to the intensive study of pattern formation in fractal media.
YAN Jia
,
FENG Fan
,
ZHANG Yongliang
,
HE Yafeng
. Pattern formation induced by subdiffusion in Oregonator model[J]. Journal of Hebei University(Natural Science Edition), 2017
, 37(1)
: 19
-23
.
DOI: 10.3969/j.issn.1000-1565.2017.01.004
[1] 欧阳颀.非线性科学与斑图动力学导论[M].北京:北京大学出版社,2010.
[2] BANSAGI JR T,VANAG V K,EPSTEIN I R.Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns [J].Science,2011,331:1309.DOI:10.1126/science.1200815.
[3] SACHS C,HILDEBRAND M,VOLKENING S,et al.Spatiotemporal self-organization in a surface reaction:from the atomic to the mesoscopic scale [J].Science,2001,31:1635.DOI:10.1126/science.1062883.
[4] 辛厚文.分形介质反应动力学[M].上海:上海科技教育出版社,1997:18.
[5] METZLER R,KLAFTER J.The random walk's guide to anomalous diffusion:A fractional dynamics approach [J].Phys Rep,2000,339:1.DOI:10.1103/PhysRevE.62.2555.
[6] DRAZER G,ZANETTE D H.Experimental evidence of power law trapping time distributions in porous media [J].Phys Rev E,1999,60:5858.DOI:10.1103/PhysRevE.60.5858.
[7] WEEKS E R,WEITZ D A.Subdiffusion and the cage effect studied near the colloidal glasstransition,Chem [J].Phys,2002,284:361.DOI:10.1103/PhysRevLett.89.095704.
[8] HERNANDEZ D,VAREA C,BARRIO R A.Dynamics of reaction diffusion systems in a subdiffusive regime [J].Phys Rev E,2009,79:026109.DOI:10.1103/PhysRevE.79.026109.
[9] GAFIYCHUKV V,DATSKO B Y.Stability analysis and oscillatory structures in time-fractional reaction-diffusion systems [J].Phys Rev E,2007,75:055201.DOI:10.1103/PhysRevE.75.055201.
[10] BERTRAM M,MIKHAILOV A S.Pattern formation on the edge of chaos:Mathematical modeling of CO oxidation on a Pt(110)surface under global delayed feedback[J].Phys Rev E,2003,67:036207.DOI:10.1103/PhysRevE.67.036207.
[11] HENRY B I,LANGLANDST A M,WEARNE S L.Anomalous diffusion with linear reaction dynamics:From continuous time random walks to fractional reaction-diffusion equations[J].Phys Rev E,2006,74:031116.DOI:10.1103/PhysRevE.74.031116.
[12] HENRY B I,LANGLANDS T A M,WEARNE S L.Turing pattern formation in fraction activator-inhibitor systems [J].Phys Rev E,2005,72:026101.DOI:10.1103/PhysRevE.72.026101.
[13] LANDLANDS A M,HENRY B I,WEARNE S L.Turing pattern formation with fractional diffusion and fractional reactions [J].Phys Condens Matter,2007,19:065115.DOI:10.1088/0953-8984/19/6/065115.
[14] GAFIYCHUK V V,DATSKO B Y.Spatiotemporal pattern formation in fractional reaction-diffusion systems with indices of different order[J].Phys Rev E,2008,77:066210.DOI:10.1103/PhysRevE.77.066210.
[15] GAFIYCHUK V V,DATSKO B Y.Pattern formation in a fractional reaction-diffusion system [J].Physica A,2006,365:300.DOI:10.1016/j.physa.2005.09.046.
[16] DASTKO B Y,GAFIYCHUK V V.Self-organization phenomena in reaction diffusion systems with non-integer order time derivatives [J].Phys Scr,2009,136:014027.DOI:10.1088/0031-8949/2009/T136/014027.
