Related papers: Revisiting the Human and Nature Dynamics model
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
We consider the dynamics of a population spatially structured in colonies that are vulnerable to catastrophic events occurring at random times, which randomly reduce their population size and compel survivors to disperse to neighboring…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
We present a novel approach to modeling market dynamics using ordinary differential equations that explicitly incorporates product competitiveness and consumer behavior. Our framework treats market segments as interacting populations in a…