Foundations of complex systems: Nonlinear dynamic, by Gregoire Nicolis PDF

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By Gregoire Nicolis

ISBN-10: 9812700439

ISBN-13: 9789812700438

ISBN-10: 981277565X

ISBN-13: 9789812775658

Complexity is rising as a post-Newtonian paradigm for forthcoming a wide physique of phenomena of outrage on the crossroads of actual, engineering, environmental, existence and human sciences from a unifying viewpoint. This publication outlines the principles of contemporary complexity learn because it arose from the cross-fertilization of rules and instruments from nonlinear technological know-how, statistical physics and numerical simulation. it's proven how those advancements bring about an figuring out, either qualitative and quantitative, of the complicated platforms encountered in nature and in daily adventure and, conversely, how traditional complexity acts as a resource of suggestion for growth on the basic point.

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Extra resources for Foundations of complex systems: Nonlinear dynamic, statistical physics, information and prediction

Example text

But when it is discovered after the poorer one, it is only weakly exploited. This establishes the primordial importance of the longrange cooperativity induced by the presence of the trail. It is tempting to conjecture that far from being a curiosity the above phenomenon, which shares with the Rayleigh-B´enard instability the property of spontaneous emergence of an a priori highly unexpected behavioral pattern, is prototypical of a large class of systems, including socio-economic phenomena in human populations (see also Sec.

6) and the like, these equations are to be seen as models, established empirically or proposed ad hoc to be verified at a later stage by experiment. ). This point is taken up further in Sec. 7. 3 Thermodynamic formulation The advantage of disposing of a description like the macroscopic description, limited to a small set of key variables, is gained at the considerable expense that the universality of the microscopic description is here lost. To begin with the structure of the equations seems to be system or model-dependent, 39 Deterministic View contrary to that of the microscopic description.

A simple example of conservative dynamical system is the frictionless pendulum. The corresponding phase space is two-dimensional and is spanned by the particle’s position and instantaneous velocity. Each trajectory with the exception of the equilibrium state on the downward vertical is an ellipse, and there is a continuum of such ellipses depending on the total energy (a combination of position and velocity variables) initially conferred to the system. 2 Dissipative systems Dissipative systems are defined by the property that the dynamics leads to eventual contraction of the volume of an initial phase space region.

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Foundations of complex systems: Nonlinear dynamic, statistical physics, information and prediction by Gregoire Nicolis

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