The proposed research project focuses on a generalization of Cellular Automata (CA) describable using both ODE and random differential equations (RDE). They are models capable of quantitative forecast as well as the same modelling flexibility of classical CA.
The use of a continuum state space permits to use new ideas about model’s calibration and validation e.g. defining a meaningful distance on the configuration space and using optimization techniques. We shall call them Interaction Based Dynamical Systems (IBDS), because they seems useful to model complex systems formed by agents locally interacting.
Objectives of the project are:
- Mathematical definition of IBDS generalizing the work done by the reintegration research group about continuum state CA modelling of urban growth
- Construction of the probability space associated to an IBDS. This is the mathematical framework where to prove the following objectives
- Study of the related differential equations. Every IBDS can be described using both an ODE, in case of infinitesimal standard deviation, and an infinite system of RDE (one for each moment of the state variables)
- Numerical solution of this system of RDE5.
- Construction of a traffic model using IBDS6.
- Numerical study of bifurcations using ODE and RDE7.
- Analysis of the possibility to generalize the MCF work of the proposal’s researcher to extend the real field adding random infinitesimal fluctuations.
- Use of this extension to study IBDS.
These objectives will be achieved using standard probability theory methods, the infinitesimals of researcher’s MCF, programming in Matlab and interdisciplinary work at the host institute.
The possibility to introduce a new and flexible type of modelling tool for the study of complex systems is of great importance both for EU and for the possibility of the researcher to obtain further future fundings for research projects, an important task of the ERG. The research project will last 4 years.
Fields of science
- natural sciencescomputer and information sciencessoftware
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations
- natural sciencesmathematicsapplied mathematicsdynamical systems
- natural sciencesmathematicsapplied mathematicsstatistics and probability
- natural sciencesmathematicsapplied mathematicsmathematical model
Call for proposal
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