Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics
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…
Logistic Models of Fractal Dimension Growth for Spatio-Temporal Dynamics of Urban Morphology
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of…
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial…
LOGISTIC MODELS OF FRACTAL DIMENSION GROWTH OF URBAN MORPHOLOGY
- Computer ScienceFractals
The principle of squashing function and empirical evidences are employed to demonstrate the following inference: the fractal dimension time series of a city’s spatial form take on a sigmoid curve, which indicates that the logistic function is the most probable selection.
Modeling growth curve of fractal dimension of urban form of Beijing
- EconomicsPhysica A: Statistical Mechanics and its Applications
Urbanization, Ikization, and Replacement Dynamics
The phenomenon of Iks was first found by anthropologists and biologists, but it is actually a problem of human geography. However, it has not yet drawn extensive attention of geographers. In this…
Mathematical Model and Computational Algorithm for Solving the Problem of the Coexistence of Different Groups of People in an Urban Environment
The article is devoted to the currently relevant problem of the development and dynamics of the population in urban formation from the point of view of spatial-dynamic approximation. The population…
An empirical examination of two-population interaction in urban growth: Tamil Nadu (1901-2011)
The urban-rural nonlinear interaction models help us to understand more about the urban system by chaos theory and meanwhile realize more the nature of chaos by urban growth. The structure of rural –…
Urban Allometric Scaling Beneath Structural Fractality of Road Networks
- HistoryAnnals of the American Association of Geographers
Allometry originally referred to the scaling relationship between the size of a body part and the size of the whole body when an organism grows. Gradually, researchers introduced it into urban…
Modeling Fractal Dimension Curve of Urban Growth in Developing Countries
The growth curve of fractal dimension of cities can be described with sigmoid function such as Boltzmann’s equation and logistic function. The logistic models of fractal dimension curves have been…
SHOWING 1-10 OF 35 REFERENCES
Modeling complex spatial dynamics of two-population interaction in urbanization process
The numerical simulation by using the discretized urban-rural population interaction model of urbanization shows a period-doubling bifurcation and chaotic behavior, which suggests that the complicated dynamics of logistic growth may come from the nonlinear interaction unbeknown to us.
Urban evolution : studies in the mathematical ecology of cities
This book develops a theory of inter- and intra-urban evolution as a branch of mathematical ecology and population dynamics. In recent years profound changes have been taking place in the methodology…
An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas
Social dynamics and the quantifying of social forces.
- SociologyProceedings of the National Academy of Sciences of the United States of America
It is shown here that the deviations are often associated with unusual intermittent events-wars, strikes, economic panics, etc-and that in many cases a few years after the event it can be abstracted as an instantaneous delta function impulse.
Growth,Innovation,Scaling and the Pace of Life in Cities
Humanity has just crossed a major landmark in its history with the majority of people now living in cities.Cities have long been known to be society's predominant engine of innovation and wealth…
Growth, innovation, scaling, and the pace of life in cities
- EconomicsProceedings of the National Academy of Sciences
Empirical evidence is presented indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times.
City Growth as a Leap-frogging Process: An Application to the Tel-Aviv Metropolis
This paper presents an analysis of the spatial and temporal development of Tel-Aviv. The central notion in the analysis is the old concept of leap-frogging. Instead of seeing the population's…