Stability of Bifurcating Patterns of Spatial Economy Models on a Hexagonal Lattice

Self-organization of spatial patterns is investigated for a scalar field of a system of locations on a hexagonal lattice. Group-theoretic bifurcation analysis is conducted to exhaustively try and f...

[1]  K. Murota,et al.  Self-organization of hexagonal agglomeration patterns in new economic geography models , 2014 .

[2]  K. Murota,et al.  Stable Economic Agglomeration Patterns in Two Dimensions: Beyond the Scope of Central Place Theory , 2017 .

[3]  A. Venables,et al.  The Spatial Economy: Cities, Regions, and International Trade , 1999 .

[4]  Michèle Sanglier,et al.  Evolutionary Models of Urban Systems: An Application to the Belgian Provinces , 1989 .

[5]  D. Stelder.  Where Do Cities Form? A Geographical Agglomeration Model for Europe , 2005 .

[6]  Anne C. Skeldon,et al.  Stability results for steady, spatially periodic planforms , 1995, patt-sol/9509004.

[7]  Tomoya Mori,et al.  On the evolution of hierarchical urban systems1 , 1999 .

[8]  K. Kirchgässner.  Exotische Lösungen des Bénardschen Problems , 1979 .

[9]  H. Stanley,et al.  Modelling urban growth patterns , 1995, Nature.

[10]  R. Lipsey,et al.  The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition , 1975 .

[11]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[12]  Kazuo Murota,et al.  Imperfect Bifurcation in Structures and Materials , 2002 .

[13]  M. Golubitsky,et al.  The Symmetry Perspective , 2002 .

[14]  Stephen L. Judd,et al.  Simple and superlattice Turing patterns in reaction-diffusion systems: bifurcation, bistability, and parameter collapse , 1998, patt-sol/9807002.

[15]  W Weidlich,et al.  Settlement formation , 1990 .

[16]  Jacques-François Thisse,et al.  A new economic geography model of central places , 2011 .

[17]  W Weidlich,et al.  A dynamic phase transition model for spatial agglomeration processes. , 1987, Journal of regional science.

[18]  P. Nijkamp,et al.  Self-Organisation in Spatial Systems—From Fractal Chaos to Regular Patterns and Vice Versa , 2015, PloS one.

[19]  Rikard Forslid,et al.  An analytically solvable core-periphery model , 2003 .

[20]  T. Akamatsu,et al.  Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models , 2012 .

[21]  Martin Golubitsky,et al.  Planforms in two and three dimensions , 1992 .

[22]  Steven Brakman,et al.  The Return of Zipf: Towards a Further Understanding of the Rank‐Size Distribution , 1999 .

[23]  Kiyohiro Ikeda,et al.  Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities , 2009 .

[24]  D. Sattinger.  Group representation theory, bifurcation theory and pattern formation , 1978 .

[25]  Alan Wilson,et al.  THE DYNAMICS OF URBAN SPATIAL STRUCTURE: PROGRESS AND PROBLEMS* , 1983 .

[26]  Kazuo Murota,et al.  Self-Organization of LöSCH's Hexagons in Economic agglomeration for Core-periphery Models , 2012, Int. J. Bifurc. Chaos.

[27]  M. Golubitsky,et al.  Bifurcation on the hexagonal lattice and the planar Bénard problem , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.