By Gregoire Nicolis, Vasileios Basios
This quantity offers a self-contained survey of the mechanisms presiding details processing and communique. the most thesis is that chaos and complexity are the fundamental elements permitting structures composed of fascinating subunits to generate and procedure info and speak in a significant approach. Emphasis is put on conversation within the type of video games and at the comparable factor of choice making lower than stipulations of uncertainty. organic, cognitive, actual, engineering and societal platforms are approached from a unifying viewpoint, either analytically and through numerical simulation, utilizing the tools of nonlinear dynamics and chance thought. Epistemological concerns in reference to incompleteness and self-reference also are addressed.
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Additional info for Chaos, Information Processing and Paradoxical Games: The Legacy of John S Nicolis
13. V. Franceschini, A Feigenbaum Sequence of Bifurcations in the Lorenz Model, J. Stat. Physics 22 397 (1980). page 40 November 14, 2014 6:16 Chaos, Information Processing and Paradoxical Games:. . 9in x 6in Scaling Properties of Lorenz System and Dissipative Nambu Mechanics b1867-ch02 41 14. C. Fowler, Analysis of the Lorenz Equations for Large r, Studies in Applied Mathematics, Elsevier Science Publishing Co, 215 (1984). 15. P. Manneville and Y. Pommeaux, Diﬀerent Ways to Turbulence in Dissipative Systems Physica 1D (1980) 219.
9in x 6in b1867-ch02 M. Axenides and E. 6 4. On the Scale Invariant Lorenz System In the last part of this work we introduce a form of the -Lorenz system which is by construction invariant under the scalings in Eqs. (20)–(21). To this end we deﬁne new independent and dependent variables (r > 2 ): τ= r− 2 t, X=√ x r− 2 , Y = y r− 2 , Z= z r− 2 (33) which satisfy the system of equations: X˙ = σ(Y − ζX), Y˙ = X(1 + ζ 2 − Z) − ζY, ζ˙ = XY − bζZ (34) with ζ = √r− 2 The derivative “dot” is with respect to the new time τ .
This is feasible through a continuous dissipation strength controlling parameter . 2. Controlling Dissipation in the Lorenz System Before we study in detail the scaling properties of the extended Lorenz system (we shall refer to it as the -Lorenz system) x˙ = σ(y − x) y˙ = x(r − z) − y (9) z˙ = xy − bz. We analyze the stability properties of its critical points. On this issue we keep in mind that a similar model has been considered in the literature9,10,12 but with precisely ﬁxed control parameter = √1σr , in order that the limit r → ∞ becomes explicit.