Related papers: The Concept of Force in Population Dynamics
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…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
A new approach is developed to understand stability of a population and further understanding of population momentum.
We investigate a class of models for opinion dynamics in a population with two interacting families of individuals. Each family has an intrinsic mean field "Voter-like" dynamics which is influenced by interaction with the other family. The…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We give a direct proof of well-posedness of solutions to general selection-mutation and structured population models with measures as initial data. This is motivated by the fact that some stationary states of these models are measures and…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
This paper develops a general force-based pedestrian model named CosForce, in which cosine functions are employed to describe asymmetric interactions. These functions implicitly capture the mechanisms of anticipation and reaction. By…
The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics,…
The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for…
Human societies around the world interact with each other by developing and maintaining social norms, and it is critically important to understand how such norms emerge and change. In this work, we define an evolutionary game-theoretic…
It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair…
Social norms and conventions are commonly accepted and adopted behaviors and practices within a social group that guide interactions -- e.g., how to spell a word or how to greet people -- and are central to a group's culture and identity.…
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,…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Ecologists have long argued about the strength of density dependence and population regulation, respectively defined as the short-term and long-term rates of return to equilibrium. Here, I give three arguments for the intractability of…
The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market…
We develop a mathematical model to describe the persistence of rule-breaking behaviors in societies, such as traffic violations, disregard for legal restrictions and other forms of noncompliance. Using a replicator-type dynamics with…
Dynamics of species' abundances in ecological communities are often described using models that only account for a few species. It is not clear when and why this would be possible, as most species form part of diverse ecological…