Foundations Of Complex Systems Nonlinear Dynamics Statistical Physics Information And Prediction 1st Edition by Gregoire Nicolis ISBN 9812700439 9789812700438

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Product details:

ISBN 10: 9812700439

ISBN 13: 978-9812700438

Author:  Gregoire Nicolis 

Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction 1st Edition: Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level.

 

Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction 1st Edition Table of contents:

The phenomenology of complex systems

• Complexity, a new paradigm
• Signatures of complexity
• Onset of complexity
• Four case studies
  • Rayleigh-Bénard convection
  • Atmospheric and climatic variability
  • Collective problem solving: food recruitment in ants
  • Human systems
• Summing up

Deterministic view

• Dynamical systems, phase space, stability
  • Conservative systems
  • Dissipative systems
• Levels of description
  • The microscopic level
  • The macroscopic level
  • Thermodynamic formulation
• Bifurcations, normal forms, emergence
• Universality, structural stability
• Deterministic chaos
• Aspects of coupling-induced complexity
• Modeling complexity beyond physical science

The probabilistic dimension of complex systems

• Need for a probabilistic approach
• Probability distributions and their evolution laws
• The retrieval of universality
• The transition to complexity in probability space
• The limits of validity of the macroscopic description
  • Closing the moment equations in the mesoscopic description
  • Transitions between states
  • Average values versus fluctuations in deterministic chaos
• Simulating complex systems
  • Monte Carlo simulation
  • Microscopic simulations
  • Cellular automata
  • Agents, players, and games
• Disorder-generated complexity

Information, entropy and selection

• Complexity and information
• The information entropy of a history
• Scaling rules and selection
• Time-dependent properties of information: information entropy and thermodynamic entropy
• Dynamical and statistical properties of time histories: large deviations, fluctuation theorems
• Further information measures: dimensions and Lyapunov exponents revisited
• Physical complexity, algorithmic complexity, and computation
• Summing up: towards a thermodynamics of complex systems

Communicating with a complex system: monitoring, analysis and prediction

• Nature of the problem
• Classical approaches and their limitations
  • Exploratory data analysis
  • Time series analysis and statistical forecasting
  • Sampling in time and in space
• Nonlinear data analysis
  • Dynamical reconstruction
  • Symbolic dynamics from time series
  • Nonlinear prediction
• The monitoring of complex fields
  • Optimizing an observational network
  • Data assimilation
• The predictability horizon and the limits of modeling
  • The dynamics of growth of initial errors
  • The dynamics of model errors
  • Can prediction errors be controlled?
• Recurrence as a predictor
  • Formulation
  • Recurrence time statistics and dynamical complexity
• Extreme events
  • Formulation
  • Statistical theory of extremes
  • Signatures of a deterministic dynamics in extreme events
  • Statistical and dynamical aspects of the Hurst phenomenon

Selected topics

• The arrow of time
  • The Maxwell-Boltzmann revolution, kinetic theory, Boltzmann’s equation
  • First resolution of the paradoxes: Markov processes, master equation
  • Generalized kinetic theories
  • Microscopic chaos and nonequilibrium statistical mechanics
• Thriving on fluctuations: the challenge of being small
  • Fluctuation dynamics in nonequilibrium steady states revisited
  • The peculiar energetics of irreversible paths joining equilibrium states
  • Transport in a fluctuating environment far from equilibrium
• Atmospheric dynamics
  • Low order models
  • More detailed models
  • Data analysis
  • Modeling and predicting with probabilities
• Climate dynamics
  • Low order climate models
  • Predictability of meteorological versus climatic fields
  • Climatic change
• Networks
  • Geometric and statistical properties of networks
  • Dynamical origin of networks
  • Dynamics on networks
• Perspectives on biological complexity
  • Nonlinear dynamics and self-organization at the biochemical, cellular, and organismic level
  • Biological superstructures
  • Biological networks
  • Complexity and the genome organization
  • Molecular evolution
• Equilibrium versus nonequilibrium in complexity and self-organization
  • Nucleation
  • Stabilization of nanoscale patterns
  • Supramolecular chemistry
• Epistemological insights from complex systems
  • Complexity, causality, and chance
  • Complexity and historicity
  • Complexity and reductionism
  • Facts, analogies, and metaphors

 

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