Chapter 3 Chaotic and noisy

Is it determined?

Extreme sensitivity

Order in the midst

Logistics and ecology

Universality

When it becomes natural

Colors of noise

Referencias y comentarios:

· Useful generic bibliography for this chapter is:

® Sync: The emerging science of spontaneous order, Steven H. Strogatz (Hyperion, New York 2003),

® Chaos and fractals, Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe (Springer, Berlin, 2004),

and others to be mentioned latter.

· For an account on how irregular behavior in basic equations may induce observable complexity, with references to the so-called dynamical systems theory, the relevant mathematics to describe chaos, see

® “Nondeterminism in the limit of nonsmooth dynamics”, Mike R. Jeffrey, Physical Review Letters 106, 254103 (2011) and its popularization in the web site: physics.aps.org/story/v28/st1.

· On trajectories, see hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra2.

· For the three body problem, www.scholarpedia.org/article/three_body_problem and

® The Three-Body Problem, Mauri Valtonen and Hannu Karttunen (Cambridge University Press, Cambridge, UK 2006)

and, for a description of the Solar System, en.wikipedia.org/wiki/solar_system, and the links therein.

· Concerning chaos, see the original description

® The Essence of Chaos, Eduard Lorenz (University of Washington Press, Washington 1993).

· For the convection of heat: theory.uwinnipeg.ca/mod_tech/node76.html and hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html.

· See a video with demonstrations of chaos, in the web site (slow download) ecommons.library.cornell.edu/handle/1813/97.

See also

® Chaos: making a new sciences, James Gleick (Viking, Nueva York 1989);

® Nonlinear Dynamics, A Two Way Trip from Physics to Math, Hernán G. Solari, Mario A. Natiello and Gabriel B. Mindlin (Institute of Physics Pub., Bristol 1996);

® Fractals and Chaos: An Illustrated Course, Paul S. Addison (Institute of Physics Pub., Bristol 1997);

® Chaos − A Program Collection for the PC, Hans J. Korsch, Hans J. Jodl, and Timo Hartmann (Springer, Berlin 2008);

brain.cc.kogakuin.ac.jp/~kanamaru/chaos/e/ and www.aw-bc.com/ide/idefiles/ navigation/toolindexes/27.htm#27.

· Robert May ha resaltado la importancia pedagógica de estudiar sistemas no-lineales sencillos para compensar la intuición lineal, inapropiada en muchas situaciones, que proporciona la educación tradicional. La referencia original es

® “Simple mathematical models with very complicated dynamics”, Robert M. May, Nature 261, 459 (1976)

· A simple treatment of chaos (and its relation with fractals), in

® Nonlinear Physics for Beginners, Lui Lam (World Scientific, Singapore 1998), which contains a copy of several original works and examples.

There is a short course, in staff.science.nus.edu.sg/~parwani/c1/node24.html, and chaos in the pendulum in: www.physics.orst.edu/~rubin/nacphy/java_pend/.

· On the possible relationship between chaos and health:

– “Evidence for determinism in ventricular fibrillation“, Francis X. Witkowski et al., Physical Review Letters 75, 1230 (1995);

– “Synchronization and rhythmic processes in physiology”, Leon Glass, Nature 410, 277 (2001);

– “Differences in the activation patterns between sustained and self-terminating episodes of human ventricular fibrillation”, Timo H. Mäkikallio et al., Annals of Medicine 34, 130 (2002);

– “Nonlinear dynamics, complex systems, and the pathobiology of critical illness”, Timothy G. Buchman, Current Opinion in Critical Care 10, 378 (2004);

– “Mathematical adventures in biology”, Michael W. Deem, Physics Today (January 2007), page 42;

– Particularmente relevante aquí es la discusión en “Nonlinear dynamics of heart rhythm disorders”, Alain Karma and Robert F. Gilmour Jr., Physics Today (March 2007), page 51, donde se describe con detalle la aparición de señales de caos en electrocardiogramas.

– Recomendamos “Synchronization and rhythmic processes in physiology”, por Leon Glass, publicado en Nature 410, 277 (2001). Véanse también las referencias al capítulo 7.

– A veces se habla (véase, por ejemplo, el comentario Controlling Cardiac Chaos - Physics News Update 840) de esfuerzos por evitar el comportamiento caótico en los ritmos cardíacos, que actualmente se consideran importantes para un comportamiento saludable. Sin embargo, se trata del uso coloquial, no técnico, del término “caos” en un contexto científico.

· To determine the existence of determinism in random series of any origin, see: sprott.physics.wisc.edu/cda.htm.

· Colored noises are described (and can even be listened to) on: en.wikipedia.org/wiki/colors_of_noise.

Nota: véanse las referencias y enlaces que se incluyen en las dispositivas del curso, que a menudo completan las anteriores.