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Complexity and control. Towards a rigorous behavioral theory of complex dynamical systems. (English) Zbl 1321.93001

In this book of 589 pages the authors aim to introduce in the literature a novel and rigorous contribution to modern Complexity Theory. It is designed to be a graduate-level monograph. The book’s content is divided into 11 chapters. Chapter 1: Introduction. Chapter 2: Local Geometrical Machinery for Complexity and Control. Chapter 3: Global Categorical Framework for Complexity and Control. Chapter 4: Dynamics of Crowd Behaviors: from complex plane to quantum random fields. Chapter 5: Hierarchical Self-Similarity in Group and Crowd Behaviors. Chapter 6: Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes. Chapter 7: Complexity and Control in Solitary Conductive PDEs. Chapter 8: Quantum-Computation for Perceptual Control Architecture. Chapter 9: Complexity and Control in Entropic and Stochastic Self-Organization. Chapter 10: Crash Simulator: Brain-and-Spine Injury Mechanisms. Chapter 11: Conclusion.
The book’s content is written in an appealing manner without useless complications. Codes from Mathematica are used in the book. I recommend the book for students and researchers interested in studying complex systems.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93D20 Asymptotic stability in control theory
81P68 Quantum computation
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