A strong demand has been recently expressed in many disciplines of the European scientific area for the interdisciplinary development of modelling approaches to complex systems. A system is said to be complex when the knowledge of every individual is not enough to apprehend its global behaviour, and the effects of collective interactions need to be incorporated. Modelling approaches consist in establishing models and in studying their behaviours by various techniques. Mathematical techniques offer a rigorous way to describe robust phenomena and identify essential characteristics. Nonlinear networks are the generic models of complex systems. A central issue in their theory is to mathematically address the dynamics in arbitrary regimes of individual and collective factor strengths. So far, this problem has only been partly solved, in extreme regimes. Our project aims to provide a comprehensive mathematical picture. The main training objective is to gain expertise and to develop the necessary techniques, especially the abstract theory of non-uniform hyperbolic dynamical systems. The return phase also includes applications to concrete examples of regulatory networks in System Biology. The outgoing host group has been chosen according to its excellence in the field, especially its expertise in bridging theory and applications. The research experience in US will bring the complementary skills (project management, mentoring, etc) needed to attain a leading independent position in the return host. By proving new conceptual functioning schemes in original situations, the project will contribute to the European endeavour on complex systems which has recently been fostered by the creation of interdisciplinary institutes in EU. As to System Biology, the project will contribute to theoretical foundations of clinical gene therapy as a new approach to the treatment of diseases. In particular, this is relevant to Human Health theme of FP7 collaboration programme.
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