Dynamics of urbanization: the empirical validation of the replacement hypothesis

Rao, D. N.; Karmeshu,; Jain, Vishal

doi:10.1068/b160289

Cited by 15 publications

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“…which suggests an allometric substitution. A process of logistic growth is in fact a process of replacement dynamics (Chen, 2012;Rao et al, 1989). A type of constituent elements is substituted by another type of elements, and a kind of activities is substituted with another kind of activities, and so on.…”

Section: Allometric Growth Based On Logistic Growthmentioning

confidence: 99%

“…The former is based on a process of a city's growth within a long period of time, while the latter is based on a distribution of a set of cities within a geographical region at a given time. A logistic process is a dynamical process of replacement (Chen, 2012;Rao et al, 1989). Based on logistic growth and basic measures such as city size, a new measure termed replacement quotient can be defined by the ratio of one basic measure to the difference between the measure and the capacity i.e., the maximum amount of the measure.…”

Section: Introductionmentioning

confidence: 99%

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An allometric scaling relation based on logistic growth of cities

Chen

2014

Chaos, Solitons & Fractals

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The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential allometry", which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the abovementioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed "logistic allometry". The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.Comment: 24 pages, 10 figures, 4 table

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Section: Allometric Growth Based On Logistic Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An allometric scaling relation based on logistic growth of cities

Chen

2014

Chaos, Solitons & Fractals

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“…As we know, the level of urbanization comes between 0 (or 0%) to 1 (or 100%), thus it can often be fitted to the logistic function since it has clear upper and lower limits (Chen, 2009;Chen and Xu, 2010;Karmeshu, 1988;Rao et al, 1989). For many years, the United Nations experts of urbanization employed the logistic model to predict the level of urbanization of different countries (United Nation, 2004).…”

Section: Model: From 1-d Map To 2-d Map 21 the 1-d Logistic Mapmentioning

confidence: 99%

Urban chaos and replacement dynamics in nature and society

Chen¹

2014

Physica A: Statistical Mechanics and its Applications

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Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and numerical computation, we can demonstrate that the 1-dimensional map comes from a 2-dimensional two-group interaction map. By analogy with urbanization, a general theory of replacement dynamics is presented in this paper, and the replacement process can be simulated with the 2-dimansional map. If the rate of replacement is too high, periodic oscillations and chaos will arise, and the system maybe breaks down. The replacement theory can be used to interpret various complex interaction and conversion in physical and human systems.The replacement dynamics provides a new way of looking at Volterra-Lotka's predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and so on.

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“…This process is termed "replacement" [13,14]. For example, the population in a geographical region can be divided into urban population and rural population, and urbanization is a process of rural-urban replacement of population [48]; the technologies can be divided into new ones and old ones, and technical innovation is a process of new-old technology replacement [49,50]. In fact, people can be divided into the rich and the poor, the geographical space can be divided into natural space and human space, and so on.…”

Section: Replacement Dynamicsmentioning

confidence: 99%

“…One typical substitution is the replacement of old technology by new; another typical substitution is the replacement of rural population by urban population. Urbanization is a process of population replacement, that is, the urban population substitutes for the rural population [47,48]. The components in a self-organized system, generally speaking, can be distributed into two classes, and the process of a system's evolution is a process of discarding one kind of component in favor of another kind of component.…”

Section: Replacement Dynamicsmentioning

confidence: 99%

Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics

Chen¹

2018

Chaos Theory

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Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However, urbanization dynamics indicates new explanation about it. Using mathematical derivation, numerical computation, and empirical analysis, we can explore chaotic dynamics of urbanization. The key is the formula of urbanization level. The urbanization curve can be described with the logistic function, which can be transformed into one-dimensional map and thus produce bifurcation and chaos. On the other hand, the logistic model of urbanization curve can be derived from the rural-urban population interaction model, which can be discretized to a two-dimensional map. An interesting finding is that the two-dimensional rural-urban coupling map can create the same bifurcation and chaos patterns as those from the one-dimensional logistic map. This suggests that the urban bifurcation and chaos come from spatial interaction between rural and urban populations rather than pure intrinsic randomicity of determinate models. This discovery provides a new way of looking at origin and essence of bifurcation and chaos in physical and social sciences.

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Dynamics of urbanization: the empirical validation of the replacement hypothesis

Cited by 15 publications

References 0 publications

An allometric scaling relation based on logistic growth of cities

An allometric scaling relation based on logistic growth of cities

Urban chaos and replacement dynamics in nature and society

Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics

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