Manuscript Topics

For better understanding the dynamics of complex real-world systems arising in various domains, the mathematician modeler is often confronted to the challenge of considering multiple scales of time, space or population, which implies to couple several formalisms, involving, among others, continuous and discrete models, deterministic and probabilistic models, microscopic and macroscopic models.

In recent years, the scientific research on such complex systems has encountered a rapidly growing interest, and numerous original questions are still left open. In particular, controlling the rich dynamics emerging in these models represents a major challenge.

This special issue is precisely focused  on the mathematical modeling and optimal control of complex systems, complex networks, multi-scale and hybrid models and their applications to a wide range of scientific domains, including physics, chemistry, engineering, mechanics, biology, population dynamics, earth sciences, ecology or epidemiology. Original research papers of high quality studying innovative models, with the aim to couple several formalisms or modeling approaches, will be considered for publication after a peer-reviewed process. Theoretical and numerical analyses of these models are both welcomed.

Topics of interest include (but are not limited to): mathematical modeling; mathematical analysis; optimal control; numerical methods; complex systems; complex networks, social networks, geographical networks; ODEs, PDEs; multi-agent systems, cellular automata; hybrid models, multi-scale models.

Applications: physics; chemistry; mechanics; engineering; population dynamics; sociology; life sciences; earth sciences; ecology; epidemiology.

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