Deterministic Chaos: Sensitivity, Mixing, and Periodic Points

1992 ◽  
pp. 117-193
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Deterministic Chaos ◽  
Periodic Points

Deterministic Chaos: Sensitivity, Mixing, and Periodic Points

2004 ◽  
pp. 467-540
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Deterministic Chaos ◽  
Periodic Points

Deterministic Chaos: Sensitivity, Mixing, and Periodic Points

1992 ◽  
pp. 507-583 ◽  
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Deterministic Chaos ◽  
Periodic Points

Complexity Measures of Brain Electrophysiological Activity

2010 ◽  
Vol 24 (2) ◽  
pp. 131-135 ◽  
Author(s):  
Włodzimierz Klonowski ◽  
Pawel Stepien ◽  
Robert Stepien
Keyword(s):  
Brain Activity ◽  
Deterministic Chaos ◽  
Epileptic Seizures ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Complexity Measures ◽  
Electrophysiological Activity ◽  
Signal Complexity ◽  
Physiological Sleep ◽  
The Brain

Over 20 years ago, Watt and Hameroff (1987 ) suggested that consciousness may be described as a manifestation of deterministic chaos in the brain/mind. To analyze EEG-signal complexity, we used Higuchi’s fractal dimension in time domain and symbolic analysis methods. Our results of analysis of EEG-signals under anesthesia, during physiological sleep, and during epileptic seizures lead to a conclusion similar to that of Watt and Hameroff: Brain activity, measured by complexity of the EEG-signal, diminishes (becomes less chaotic) when consciousness is being “switched off”. So, consciousness may be described as a manifestation of deterministic chaos in the brain/mind.

FIRST OBSERVATION OF DETERMINISTIC CHAOS IN PASSIVE Q-SWITCHING PULSATION

1988 ◽  
Vol 49 (C2) ◽  
pp. C2-413-C2-416
Author(s):  
M. TACHIKAWA ◽  
K. TANII ◽  
F.-L. HONG ◽  
T. TOHEI ◽  
M. KAJITA ◽  
...  
Keyword(s):  
Deterministic Chaos ◽  
Q Switching

scholarly journals Nature, Nurture, and Noise: Developmental Instability, Fluctuating Asymmetry, and the Causes of Phenotypic Variation

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1204
Author(s):  
John H. Graham
Keyword(s):  
Fluctuating Asymmetry ◽  
Phenotypic Variation ◽  
Deterministic Chaos ◽  
Monozygotic Twins ◽  
Developmental Instability ◽  
Nonlinear Feedback ◽  
Developmental Variation ◽  
Sewall Wright ◽  
Developmental Noise ◽  
And Behavior

Phenotypic variation arises from genetic and environmental variation, as well as random aspects of development. The genetic (nature) and environmental (nurture) components of this variation have been appreciated since at least 1900. The random developmental component (noise) has taken longer for quantitative geneticists to appreciate. Here, I sketch the historical development of the concepts of random developmental noise and developmental instability, and its quantification via fluctuating asymmetry. The unsung pioneers in this story are Hugo DeVries (fluctuating variation, 1909), C. H. Danforth (random variation between monozygotic twins, 1919), and Sewall Wright (random developmental variation in piebald guinea pigs, 1920). The first pioneering study of fluctuating asymmetry, by Sumner and Huestis in 1921, is seldom mentioned, possibly because it failed to connect the observed random asymmetry with random developmental variation. This early work was then synthesized by Boris Astaurov in 1930 and Wilhelm Ludwig in 1932, and then popularized by Drosophila geneticists beginning with Kenneth Mather in 1953. Population phenogeneticists are still trying to understand the origins and behavior of random developmental variation. Some of the developmental noise represents true stochastic behavior of molecules and cells, while some represents deterministic chaos, nonlinear feedback, and symmetry breaking.

Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c

1994 ◽  
Vol 101 (4) ◽  
pp. 318 ◽  
Author(s):  
Ralph Walde ◽  
Paula Russo
Keyword(s):  
Quadratic Function ◽  
Periodic Points

scholarly journals Deterministic chaos in an ytterbium-doped mode-locked fiber laser

2018 ◽  
Vol 26 (10) ◽  
pp. 13686 ◽  
Author(s):  
Lucas B. A. Mélo ◽  
Guillermo F. R. Palacios ◽  
Pedro V. Carelli ◽  
Lúcio H. Acioli ◽  
José R. Rios Leite ◽  
...  
Keyword(s):  
Fiber Laser ◽  
Deterministic Chaos

scholarly journals A topological lens for a measure-preserving system

2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS
Keyword(s):  
Topological Entropy ◽  
Periodic Points ◽  
Positive Entropy ◽  
Topological Properties ◽  
Topologically Transitive ◽  
Topological System ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Dynamical Properties

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).

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