Biomedical subjects
Publications and source records attributed to PM Binder.
We study systematically what levels of finite-resolution in measurements significantly affect the calculation of time delays, embedding dimensions, and Lyapunov exponent for two well-known chaotic systems. We find a tradeoff between the information contained in the measured time series and what is lost. Moreover, the "noise" series is low-dimensional and highly correlated.
The connection between an observer-based theory of measurement and a hierarchical classification of complex systems in terms of topological exponents is discussed. This leads to generalized definitions of complexity that capture different aspects of the structure of the trajectory space of complex systems.
The measure of complexity recently proposed by Shiner, Davidson, and Landsberg [Phys. Rev. E 59, 1459 (1999)] does not adequately describe the transition from regular to indexed languages observed at the period-doubling accumulation points of quadratic maps. This Comment points to a generic inadequacy of that measure.
A symbolic dynamics of the Markov chain model for trajectories of the kicked rotor (standard map) in sticky regions near resonant orbits is developed. Two sets of trajectories are shown to correspond to a context-free and a context-sensitive language, respectively.
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