Project deals with novel advanced methods for global analysis and control design for decomposed strongly nonlinear state space dynamical models with complex interactions of their components. Focus will be made on multivalued uncertain dynamical systems, especially the multivalued systems class that might be called as the "systems of systems". The aim is to investigate the chaotic behavior of particular subsystems and their mutual interactions, special stress would be made on case when their boundary varies with time. Further, global analysis of the solution set would be provided, depending on real system parameters and eventually on control variable. Principal approach here is based on structural methods, nonlinear transformations and decompositions into particular, though complex interconnected systems. Topological Morse decomposition and the multivalued Conley index theory will be used for the corresponding global analysis. Results may serve as a basis for further development of numerical algorithms for practical problems in important areas like systems biology.