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Complexity: Hierarchical Structures and Scaling in Physics
TLDR
Part I. Phenomenology and Models: Examples of complex behaviour and Mathematical models and Thermodynamic formalism.
Characterizing dynamics with covariant Lyapunov vectors.
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of
Measuring spike train synchrony
Covariant Lyapunov vectors
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of
From anomalous energy diffusion to levy walks and heat conductivity in one-dimensional systems
The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy
Dynamic localization of Lyapunov vectors in spacetime chaos
We study the dynamics of Lyapunov vectors in various models of one-dimensional distributed systems with spacetime chaos. We demonstrate that the vector corresponding to the maximum exponent is always
Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors
The analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems. Prominent roles in our approach are played by the generalized
Desynchronization in diluted neural networks.
TLDR
The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated, and the paradox is solved by drawing an analogy with the phenomenon of "stable chaos" by observing that the stochasticlike behavior is "limited" to an exponentially long transient.
Renormalization of correlations and spectra of a strange non-chaotic attractor
We study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum. We show that the symbolic dynamics is exactly described by a language
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