相关论文: Nonlinear Autoregressive Approach to Estimating Lo…
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of…
Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal…
The time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the growth rate formula and…
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 fractal dimension of urban form can be…
Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension…
The growth curves of fractal dimension of urban form take on squashing effect and can be described by sigmoid functions. The fractal dimension growth of urban form in western countries can be modeled by Boltzmann's equation and logistic…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
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 replacement dynamics of urban evolution.…
Entropy is one of physical bases for fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using fractal dimension, we can describe urban growth and form and characterize spatial complexity. A…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
This study investigates city dynamics employing a nonextensive diffusion equation suited for addressing diffusion within a fractal medium, where the nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the efficacy of…
This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to explain the fractal dimension of urban form. The…
The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…