Foundations of Complex Systems Emergence, Information and Prediction

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science. Contents:The Phenomenology of Complex Systems:Complexity, a New ParadigmSignatures of ComplexityOnset of ComplexityFour Case StudiesSumming UpDeterministic View:Dynamical Systems, Phase Space, StabilityLevels of DescriptionNormal FormsThe Limit of UniversalityDeterministic ChaosEmergenceCoupling-Induced ComplexityModeling Complexity Beyond Physical ScienceProbabilistic Description:Need for a Probabilistic ApproachProbability Distributions and Their Evolution LawsThe Retrieval of UniversalityComplexity in the Probabilistic DescriptionEmergence RevisitedTransitions Between StatesSimulating Complex SystemsDisorder-Generated ComplexityComplexity, Entropy and Information:Information EntropyDynamical EntropiesInformation Entropy ProductionLarge Deviations, Fluctuation Theorems and the Probabilistic Properties of Time SequencesAlgorithmic Complexity and ComputationDynamical Systems as Information Sources: Scaling Rules and SelectionFurther Information MeasuresSumming UpPrediction:Communicating with a Complex SystemClassical Approaches and Their LimitationsNonlinear Data AnalysisThe Monitoring of Complex FieldsThe Predictability HorizonRecurrenceExtreme EventsSelected Topics:The Arrow of TimeNanosystemsAtmospheric DynamicsClimate DynamicsNetworksPerspectives on Biological ComplexityEquilibrium Versus Nonequilibrium in Complexity and Self-OrganizationEpistemological Insights from Complex SystemsOutlook. The Future of Complexity Readership: Graduate students, researchers, academics and professionals interested in nonlinear science. Keywords:Nonlinear Dynamics;Chaos;Self-Organization;Emergence;Probability and Information;Predictability;Non-Equilibrium Systems;Irreversibility;Systems BiologyKey Features:A unique vision highlighting complexity as part of fundamental science and a clear, unifying presentation of the concepts and tools needed to analyze complex systemsIllustrates the interdisciplinary dimension of complexity research through representative examples pertaining to problems of current concernNew edition, including a large collection of exercises and problems with hints for solution and an updated survey of the literatureReviews: “The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of the field.” Zentralblatt MATH