Diffusion Models on Networks
In this research project diffusion models on networks are studied. A complex network can be thought of as a large dynamical model composed of smaller dynamical systems, and these smaller dynamical systems interact with each other over a network topology. Examples include consensus dynamics, physical diffusion models, virus propagation and economic models that study how the market adopts a new product or technology. When we add humans to the loop, this makes the study unpredictable and uncertain, and there is a lot of research to be done in this direction.
In the study of consensus dynamics we have a large population of individuals and these individuals communicate with each other. Everyone has a certain opinion or belief, and by communication or interaction with other fellows it can happen that one changes their opinion. It is of interest to study whether this group of people reach a common opinion after a period of time, such that everyone shares the same believe.
In virus propagation models we can think of how a disease spreads over a network. Here, infection takes place through spontaneous infection or by interaction with infected individuals. It is of interest whether these models converge to a steady-state eventually, and whether this depend on the topology of the underlying network.
Diffusion models also appear in economic models. Here we can think of manufacturers that produce similar products or goods, and these manufacturers compete with each other for the largest market share. The market share can be thought of as the fraction of buyers or consumers committed to that option. We investigate how the dynamics of the system change if we assume that people are crowd-seeking, which means they will adopt the product that is used by most of the people with whom they interact. We can also study the role of advertisements done by a company, which lures consumers of competing companies. This model originates from a biological model.
In virus propagation models we can think of how a disease spreads over a network. Here, infection takes place through spontaneous infection or by interaction with infected individuals. It is of interest whether these models converge to a steady-state eventually, and whether this depend on the topology of the underlying network.
Diffusion models also appear in economic models. Here we can think of manufacturers that produce similar products or goods, and these manufacturers compete with each other for the largest market share. The market share can be thought of as the fraction of buyers or consumers committed to that option. We investigate how the dynamics of the system change if we assume that people are crowd-seeking, which means they will adopt the product that is used by most of the people with whom they interact. We can also study the role of advertisements done by a company, which lures consumers of competing companies. This model originates from a biological model.
These typical examples will be studied in this research project, and stability and controllability results will be found by using game-theoretic tools.
| Last modified: | 27 March 2019 09.23 a.m. |