The Dynamics of Urban Spatial Structure: Some Exploratory Results Using Difference Equations and Bifurcation Theory

1981 ◽  
Vol 13 (12) ◽  
pp. 1473-1483 ◽  
Author(s):  
M Clarke ◽  
A G Wilson
Keyword(s):  
Difference Equation ◽  
Spatial Structure ◽  
Dynamic Model ◽  
Difference Equations ◽  
Bifurcation Theory ◽  
Equation Model ◽  
Urban Spatial Structure ◽  
Hypothetical System ◽  
Simple Difference ◽  
Bifurcation Behaviour

It is demonstrated that a simple difference equation model, which exhibits complex bifurcation behaviour, can be used to represent change in urban retailing and residential systems. These submodels are combined to form a rudimentary dynamic model of urban spatial structure. A sample of exploratory results are presented for a 169-zone hypothetical system.

Expansion of the subway network and spatial distribution of population and employment in the Seoul metropolitan area

Urban Studies ◽  
2017 ◽  
Vol 55 (11) ◽  
pp. 2499-2521 ◽  
Author(s):  
Jangik Jin ◽  
Danya Kim
Keyword(s):  
Spatial Structure ◽  
Metropolitan Area ◽  
Public Transportation ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Urban Spatial Structure ◽  
Urban Centre ◽  
Seoul Metropolitan Area ◽  
Job Growth ◽  
Subway System

The objective of this study is to address two questions that are pertinent to the issue of transportation and urban spatial structure. First, we investigate whether the improvement of the subway system affects the spatial structure in the Seoul metropolitan area. Second, if so, we examine whether it contributes to the suburbanisation of population and employment or spatial concentration around the urban centre. To do so, we focus on the improvement of the subway system in Seoul metropolitan areas between 2000 and 2010 with micro population and employment data. Because of the interrelationship between population, employment and transportation, we control for the interplay between population, employment and subway network by using a simultaneous equation model. Our results provide several interesting findings. First, the improvement of the subway system plays an important role in changes in urban spatial structure. Second, the improvement of the subway system significantly affects job growth in the urban centre and subcentres in the city of Seoul. Third, the interrelationship between population, employment and public transportation generates redistributive effects that are substantially associated with urban growth and decline, and determine urban spatial structure.

A Dynamic Model of Presidential Nomination Campaigns

1980 ◽  
Vol 74 (3) ◽  
pp. 651-669 ◽  
Author(s):  
John H. Aldrich
Keyword(s):  
Mathematical Model ◽  
Difference Equation ◽  
Dynamic Model ◽  
Equation Model ◽  
Electoral Success ◽  
Presidential Nomination ◽  
Dynamic Forces ◽  
Selection Of

Recent campaigns have demonstrated the importance of dynamic elements in affecting the selection of presidential nominees. This paper develops a mathematical model to analyze these dynamics. The heart of the model is the assumed relationship between the ability to acquire resources and success in primaries and caucuses. The expenditure of resources leads to greater electoral success, while greater electoral success (in particular, exceeding expectations in a primary or caucus) leads to greater resource-gathering capabilities. A difference equation model of these relationships is proposed. I prove that any campaign of this form is necessarily unstable, which implies that most candidates will be “winnowed out” necessarily, while only a very few, but at least one candidate, will necessarily “have momentum.” This result is true whether there are two or many contenders. However, I also argue that the larger the number of candidates, the stronger the dynamic forces, and thus the more rapid the “winnowing out” process.

A Predictive Model of Urban Stock and Activity: 1. Theoretical Considerations

1975 ◽  
Vol 7 (8) ◽  
pp. 965-979 ◽  
Author(s):  
M A O Ayeni
Keyword(s):  
Spatial Structure ◽  
Predictive Model ◽  
Dynamic Model ◽  
Predictive Models ◽  
Urban Systems ◽  
Urban Spatial Structure ◽  
Static Models ◽  
Theoretical Considerations

Urban systems are dynamic and hence require predictive models that incorporate the element of time more explicitly. Comparative static models of the Lowry type may be embellished by the use of the entropy-maximizing methodology and by slight reformulations of the equations by the introduction of simple lags. The result is a quasi-dynamic or dynamic model of urban spatial structure. This is the first of two papers, in which the issues involved in the construction of predictive models are discussed and the equation systems of the model developed. The operationalization of the concepts and the empirical development of the model for a Nigerian city will be discussed in the paper to follow.

Characterizing the urban spatial structure using taxi trip big data and implications for urban planning

2021 ◽  
Author(s):  
Haibo Li ◽  
Xiaocong Xu ◽  
Xia Li ◽  
Shifa Ma ◽  
Honghui Zhang
Keyword(s):  
Big Data ◽  
Urban Planning ◽  
Spatial Structure ◽  
Urban Spatial Structure

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

scholarly journals Note on some representations of general solutions to homogeneous linear difference equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Fibonacci Sequence ◽  
Linear Difference Equation ◽  
Linear Difference Equations ◽  
Second Order Difference Equation ◽  
Constant Coefficients ◽  
Order Difference Equation ◽  
Homogeneous Linear

Abstract It is known that every solution to the second-order difference equation $x_{n}=x_{n-1}+x_{n-2}=0$ x n = x n − 1 + x n − 2 = 0 , $n\ge 2$ n ≥ 2 , can be written in the following form $x_{n}=x_{0}f_{n-1}+x_{1}f_{n}$ x n = x 0 f n − 1 + x 1 f n , where $f_{n}$ f n is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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