The research problems and challenges of this research group can be mentioned using the classification proposed in 2012 by the CSS – Complex Systems Society regarding the complex systems studies domains (see “The CSS Roadmap for Complex Systems Science and its Applications 2012 – 2020”) . The items to be specifically addressed by our researchers are the following:
- Concepts and tools that deal with general dynamical systems coupled with stochastic processes
- Random dynamical systems (RDS) field provide important geometrical concepts that are appropriate and useful in the context of stochastic modeling. Yet, synchronization phenomena, stochastic bifurcations (namely, dynamical and phenomenological bifurcations), emergence of patterns (and phase transitions) and multi-scale dynamics are strictly related to RDS.
- Measures to collective behavior in homogeneous and heterogeneous systems
- Complexity of systems composed of many distinct units which display collective behavior on space end time scales manifests itself in the non-trivial properties of the dynamics. Successful modeling of that collective systems require at least the quantification of heterogeneities (at different scales), the identification of the heterogeneity features that are relevant at the global level and the study of responses to changes in these heterogeneities.
- Optimal control in complex dynamics resulting from the co-existence of multiple objectives, which may be in conflict, and projection into spaces of different dimension
- Multi-criteria methodology and dynamical optimization provides a wide number of methods to be explored and improved in decision aid. Also, dynamics are often uncertain and partially unknown, implying a difficult compromise between exploitation of the best know parts of the dynamics and of the worst known ones.
- Mathematical and computer tools formalisms for modeling multilevel and multi-scale systems
- To make explicit and meaningful connections from micro to macro levels (emergence functions) and from micro to macro levels (immergence functions) is essential to obtain a complete system dynamics with many hierarchically organized levels.
- Designing artificial complex systems
- Emergent technologies have been inspired from natural complex systems (NCS), whether physical, biological or social. Also, artificial complex systems (ACS), which are built upon intrinsically distributed, self-organizing and evolutionary entities, should be able to reproduce the original behavior and the organizational principles (cooperation and/or the competition) observed in NCS. This is the case of neural networks based on neuroscience or genetic algorithms inspired by Darwinian evolution. Although ACS can be created to schedule /model, analyze and control the NCS, in a process where they are integrated or even asynchronous, the natural-inspired artificial design is not restricted by any “fidelity” to the original NCS.
- Petascale Computing
- High Performance Computing is used for managing large-scale resources to solve grand challenge problems in computational social science.
- Formal aspects of Complex Systems Science
- Formal analysis of complex systems.
- Game theory - models, numerical methods and applications
- Physiological functions
- A complex system approach to physiological functions - which results from the integration of cells, tissues and organ properties in the context of the whole organism and its environment - should lead to an iterated cycle combining theoretical methods with relevant measurements and experimentation and tools for appropriate observing, modeling, and computer simulation.
- Ecosystemic complexity
- The multiplicity and diversity of interactions between a great number of physicochemical factors and biological entities that characterize an ecosystem, as well as their participation of a wide range of organizational levels and a broad spectrum of space and temporal scales, justify the expression of “ecosystemic complexity”.
- From individual cognition to social cognition
- Innovation, learning and co-evolution
- Territorial intelligence and sustainable development
- Machine learning, retro-action, hybrid complex systems
Education, Training and Professional Practice.