Difference between revisions of "CSSS 2008 Argentina-Readings"
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-P. Gaspard, Time-reversed dynamical entropy and irreversibility in Markovian random processes, J. Stat. Phys. 117, 599 (2004).<br /> | -P. Gaspard, Time-reversed dynamical entropy and irreversibility in Markovian random processes, J. Stat. Phys. 117, 599 (2004).<br /> | ||
[[Media: | Supporting Material: | ||
[http://www.scholarpedia.org/article/Complex_systems Complex Systems - Scholarpedia] | |||
[[Media: G_Nicolis.pdf| Interdisciplinary Center for Nonlinear Phenomena and Complex Systems - G. Nicolis]] | |||
[[Media: ERWnicolis1.pdf| Foundations of Complex Systems - G. Nicolis, C. Nicolis]] | |||
[[Media: ERWnicolisfig1.eps| Figure 1]] | |||
[[Media: ERWnicolisfig2.eps| Figure 2]] | |||
[[Media: ERWnicolisfig3.eps| Figure 3]] |
Revision as of 19:14, 4 November 2008
CSSS Argentina 2008 |
Week 1 (tentative)
- Elizabeth Bradley (Nonlinear dynamics)
Definition of chaos; examples in various fields
An extended example: the logistic map. Introduce: bifurcations; bifurcation diagram and its structure, incl. Feigenbaum number; fractals and their connection to chaos
Continuous-time dynamics: definition
Introduce concepts: state variables, state space, trajectory, initial condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter
An extended example: the Lorenz system: history, physical meaning, trajectories, attractors, bifurcations (examples & definitions), types of attractors, stability: definition & mathematics, eigen. , un/stable manifolds, Lyapunov exponent and the connection to chaos
Numerical solvers: roles and issues
Shadowing
Projection vs section
Poincare sections in space & time
Delay-coordinate embedding
Examples: roulette, the SFI competition
Applications: filtering, control of chaos, synchronization & communication, spacecraft orbits, chaos in the solar system, harnessing the butterfly effect in fluids
Week 2
References:
-G. Nicolis and C. Nicolis, Foundations of Complex Systems, World Scientific, Singapore (2007).
-W. Ebeling and G. Nicolis, Word frequency and entropy of symbolic sequences: a dynamical perspective, Chaos Solitons and Fractals 2, 635 (1992).
-G. Nicolis and P. Gaspard, Toward a probabilistic approach to complex systems, Chaos Solitons and Fractals 4, 41 (1994).
-G. Nicolis, Thermodynamics today, Physica A213, 1 (1995).
-G. Nicolis and D. Daems, Probabilistic and thermodynamic aspects of dynamical systems, Chaos 8, 311 (1998).
-G. Nicolis, Nonequilibrium Statistical Mechanics, in Encyclopedia of Nonlinear Science, A. Scott ed., Routledge, New York (2005).
-P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge University Press, Cambridge (1998).
-P. Gaspard, Time-reversed dynamical entropy and irreversibility in Markovian random processes, J. Stat. Phys. 117, 599 (2004).
Supporting Material:
Complex Systems - Scholarpedia Interdisciplinary Center for Nonlinear Phenomena and Complex Systems - G. Nicolis Foundations of Complex Systems - G. Nicolis, C. Nicolis Figure 1 Figure 2 Figure 3