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This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts.
List of contents
Part I: Chaos and Dynamics.- 1. Weak Transient Chaos.- 2. Lorenz type attractor in electronic parametric generator and its transformation outside the parametric resonance.- 3. Time Rescaling of Lyapunov Exponents.- 4. Unraveling the Chaos-land and its organization in the Rabinovich System.- 5. Anomalous transport in steady plane viscous flows: simple models.- Part II: Synchronization and Networks.- 6. Coherence-incoherence transition and properties of dierent types of chimeras in a network of nonlocally coupled chaotic maps.- 7. Regular and Chaotic Transition to Synchrony in a Star Configuration of Phase Oscillators.- 8. Lotka-Volterra like Dynamics in Phase Oscillator Networks.- 9. Intrinsic Stability, Time Delays and Transformations of Dynamical Networks.- 10. Discovering, Constructing, and Analyzing Synchronous Clusters of Oscillators in a Complex Network using Symmetries.- 11. When repulsive inhibition promotes synchrony of bursting neurons: Help from the enemy.- Part III: Brain.-12. The variational principles of cognition.- 13. Olfactory computation in insects.- 14. Respiratory Neural Network: Activity and Connectivity.- 15. Dynamics of odor-evoked activity patterns in the olfactory system.- 16. Dynamics of Intermittent Synchronization of Neural Activity.- Part IV: Waves.- 17. Vortices termination in the cardiac muscle.- 18. KDV soliton gas: interactions and turbulence.- 19. Multi-lump structures in the Kadomtsev-Petviashvili equation.
About the author
Dr. Igor Aronson is Senior Scientist and Theory Group Leader, Materials Science Division, Argonne National Laboratory, Argonne, Illinois; Dr. Arkady Pikovsky is Professor of Theoretical Physics, University of Potsdam, Potsdam, Germany; Dr. Nikolai Rulkov is Research Scientist, BioCircuits Institute at the University of California, San Diego, La Jolla, CA; and Dr. Lev S. Tsimring is Associate Director, BioCircuits Institute University of California, San Diego, La Jolla, CA.
