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

2018 ◽  
Vol 28 (11) ◽  
pp. 1850138 ◽  
Author(s):  
K. Ikeda ◽  
H. Aizawa ◽  
Y. Kogure ◽  
Y. Takayama
Keyword(s):  
Scalar Field ◽  
Economic Geography ◽  
Bifurcation Analysis ◽  
Hexagonal Lattice ◽  
Self Organization ◽  
New Economic Geography ◽  
Economy Model ◽  
Spatial Economy ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

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 find possible bifurcating patterns. All these patterns are proved to be asymptotically unstable for general spatial economic models in new economic geography. Microeconomic interactions among the locations are expressed by a spatial economy model and all bifurcating patterns are demonstrated to be unstable by numerical bifurcation analysis.

SELF-ORGANIZATION OF LÖSCH'S HEXAGONS IN ECONOMIC AGGLOMERATION FOR CORE-PERIPHERY MODELS

2012 ◽  
Vol 22 (08) ◽  
pp. 1230026 ◽  
Author(s):  
KIYOHIRO IKEDA ◽  
KAZUO MUROTA ◽  
TAKASHI AKAMATSU
Keyword(s):  
Economic Geography ◽  
Bifurcation Analysis ◽  
Hexagonal Lattice ◽  
Central Place ◽  
New Economic Geography ◽  
Central Place Theory ◽  
Place Theory ◽  
Self Organized ◽  
Population Distributions ◽  
Economic Agglomeration

Hexagonal population distributions of several sizes are shown to be self-organized from a uniformly inhabited state, which is modeled by a system of places (cities) on a hexagonal lattice. Microeconomic interactions among the places are expressed by a core-periphery model in new economic geography. Lösch's ten smallest hexagonal distributions in central place theory are guaranteed to be existent by equivariant bifurcation analysis on D 6 ∔ (ℤn × ℤn), and are obtained by computational analysis. The missing link between central place theory and new economic geography has thus been discovered in light of the bifurcation analysis.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

2010 ◽  
Author(s):  
Nalwala Rohitbabu Gangadhar ◽  
Periyasamy Balasubramanian ◽  
Swapan Paruya ◽  
Samarjit Kar ◽  
Suchismita Roy
Keyword(s):  
Bifurcation Analysis ◽  
Stirred Tank ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuously Stirred Tank Reactor ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

scholarly journals Numerical bifurcation analysis of a ?car-following? model

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 552-553
Author(s):  
Gabriele Sirito ◽  
Ingeniun Gasser ◽  
Tilman Seidel
Keyword(s):  
Bifurcation Analysis ◽  
Car Following ◽  
Car Following Model ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

Competitiveness and Polycentrism for SMEs in Bogotá Region, Colombia

2020 ◽  
pp. 54-79
Author(s):  
Luis Armando Blanco ◽  
Fabio Fernando Moscoso Duran ◽  
Julián Marcel Libreros
Keyword(s):  
Economic Development ◽  
Spatial Structure ◽  
Economic Geography ◽  
Self Organization ◽  
New Economic Geography ◽  
City Region ◽  
Central Thesis ◽  
The City ◽  
Edge Cities

This chapter studies the dynamics of Bogotá Region based on the New Economic Geography and the recent works on economic development in two big dimensions: the economic and the spatial structure; that is, productivity and polycentrism. The central thesis, supported on an econometric exercise for SMEs in 20 cities in Bogotá-Sabana region, is that with greater strength in the interior of Bogotá and less in the city region, a transition from monocentrism to functional polycentrism is consolidating. Krugman's Edge Cities model concludes that polycentrism comes from a process of spontaneous self-organization and produces a territorial order according to the mysterious ZIP law and consistent with efficiency, equity, and sustainability.

scholarly journals Of Hype and Hyperbolas: Introducing the New Economic Geography

2001 ◽  
Vol 39 (2) ◽  
pp. 536-561 ◽  
Author(s):  
J. Peter Neary
Keyword(s):  
Decision Making ◽  
General Equilibrium ◽  
Economic Geography ◽  
Building Blocks ◽  
New Economic Geography ◽  
Rational Decision ◽  
Equilibrium Models ◽  
Trade Off ◽  
Rational Decision Making ◽  
Spatial Economy

Reviewing The Spatial Economy by Fujita, Krugman, and Venables, this paper argues that the key contribution of the new economic geography is a framework in which standard building blocks of mainstream economics (especially rational decision making and simple general equilibrium models) are used to model the trade-off between dispersal and agglomeration. The approach thus gives a choice-theoretic basis for a “propensity to agglomerate.”

Numerical Bifurcation Analysis of Multimode Impact Oscillations Between a Pantograph and a Rigid Conductor Line

2012 ◽  
Author(s):  
Kiyotaka Yamashita ◽  
Tomoaki Nakayama ◽  
Toshihiko Sugiura ◽  
Hiroshi Yabuno
Keyword(s):  
Bifurcation Analysis ◽  
Numerical Technique ◽  
Single Mode ◽  
Current Collection ◽  
Conductor Line ◽  
Mode Solution ◽  
Numerical Bifurcation ◽  
The Impact ◽  
Impact Oscillations ◽  
Numerical Bifurcation Analysis

This paper deals with the numerical bifurcation analysis of the contact loss between a pantograph and an overhead rigid conductor line in a railway current collection system. In the previous study, we modeled this problem as impact oscillations of an intermediate spring-supported beam excited by an oscillating plate. We have already derived the modal interaction relationship equations that describe the velocities immediately after an impact as functions of the velocities before impact for each vibration mode. A numerical calculation using these relationship equations was performed to clarify the impact oscillations with multiple vibration modes. In this paper, we propose a numerical technique based on maps that transform the state of the system at the impact to the subsequent state at the next impact. This numerical method produces stability analyses of the fixed points of the map that describes an impact oscillation with multiple modes. These results can differ surprisingly from the expectations based on a single-mode solution. These results are compared with experiments undertaken in our laboratory, utilizing a thin stainless steel beam. The typical features of impact oscillations, which were theoretically predicted, were confirmed qualitatively.

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