Foundations of complex systems : nonlinear dynamics statistical physics, information and prediction / Gregoire Nicolis, Catherine Nicolis.

Format:

Book

Author/Creator:

Nicolis, G., 1939-

Contributor:

Nicolis, Cathy.

Language:

English

Subjects (All):

Nonlinear systems.

System analysis.

Computational complexity.

Nonlinear theories.

Physical Description:

1 online resource (344 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, N.J. : World Scientific, c2007.

Summary:

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,

Contents:

Contents; Preface; 1 The phenomenology of complex systems; 1.1 Complexity, a new paradigm; 1.2 Signatures of complexity; 1.3 Onset of complexity; 1.4 Four case studies; 1.4.1 Rayleigh-B enard convection; 1.4.2 Atmospheric and climatic variability; 1.4.3 Collective problem solving: food recruitment in ants; 1.4.4 Human systems; 1.5 Summing up; 2 Deterministic view; 2.1 Dynamical systems, phase space, stability; 2.1.1 Conservative systems; 2.1.2 Dissipative systems; 2.2 Levels of description; 2.2.1 The microscopic level; 2.2.2 The macroscopic level; 2.2.3 Thermodynamic formulation

2.3 Bifurcations, normal forms, emergence2.4 Universality, structural stability; 2.5 Deterministic chaos; 2.6 Aspects of coupling-induced complexity; 2.7 Modeling complexity beyond physical science; 3 The probabilistic dimension of complex systems; 3.1 Need for a probabilistic approach; 3.2 Probability distributions and their evolution laws; 3.3 The retrieval of universality; 3.4 The transition to complexity in probability space; 3.5 The limits of validity of the macroscopic description; 3.5.1 Closing the moment equations in the mesoscopic description; 3.5.2 Transitions between states

3.5.3 Average values versus uctuations in deterministic chaos3.6 Simulating complex systems; 3.6.1 Monte Carlo simulation; 3.6.2 Microscopic simulations; 3.6.3 Cellular automata; 3.6.4 Agents, players and games; 3.7 Disorder-generated complexity; 4 Information, entropy and selection; 4.1 Complexity and information; 4.2 The information entropy of a history; 4.3 Scaling rules and selection; 4.4 Time-dependent properties of information. Information entropy and thermodynamic entropy; 4.5 Dynamical and statistical properties of time histories. Large deviations, uctuation theorems

4.6 Further information measures. Dimensions and Lyapunov exponents revisited4.7 Physical complexity, algorithmic complexity, and computation; 4.8 Summing up: towards a thermodynamics of complex systems; 5 Communicating with a complex system: monitoring, analysis and prediction; 5.1 Nature of the problem; 5.2 Classical approaches and their limitations; 5.2.1 Exploratory data analysis; 5.2.2 Time series analysis and statistical forecasting; 5.2.3 Sampling in time and in space; 5.3 Nonlinear data analysis; 5.3.1 Dynamical reconstruction; 5.3.2 Symbolic dynamics from time series

5.3.3 Nonlinear prediction5.4 The monitoring of complex fields; 5.4.1 Optimizing an observational network; 5.4.2 Data assimilation; 5.5 The predictability horizon and the limits of modeling; 5.5.1 The dynamics of growth of initial errors; 5.5.2 The dynamics of model errors; 5.5.3 Can prediction errors be controlled?; 5.6 Recurrence as a predictor; 5.6.1 Formulation .; 5.6.2 Recurrence time statistics and dynamical complexity; 5.7 Extreme events; 5.7.1 Formulation; 5.7.2 Statistical theory of extremes; 5.7.3 Signatures of a deterministic dynamics in extreme events

5.7.4 Statistical and dynamical aspects of the Hurst phenomenon

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 291-320) and index.

ISBN:

9786611928308

9781281928306

1281928305

9789812775658

981277565X

OCLC:

879025091