Related papers: Modeling complex spatial dynamics of two-populatio…
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,…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
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…
Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating…
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
Quantifying the spatial organization of human settlements is fundamental to understanding the complexity of urban systems. However, the quantitative patterns of the distribution of villages, towns, and cities that lie between random and…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
Urban systems are composed by complex couplings of several components, and more particularly between the built environment and transportation networks. Their interaction is involved in the emergence of the urban form. We propose in this…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Urban evolution processes occur at different scales, with intricate interactions between levels and relatively distinct type of processes. To what extent actual urban dynamics include an actual strong coupling between scales, in the sense…
In 2012 the world's population exceeded 7 billion, and since 2008 the number of individuals living in urban areas has surpassed that of rural areas. This is the result of an overall increase of life expectancy in many countries that has…
In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model,…