Chaos

Crutchfield, James P.; Farmer, J. Doyne; Packard, Norman H.; Shaw, Robert S.

doi:10.1038/scientificamerican1286-46

Cited by 387 publications

(143 citation statements)

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“…Starting from X 0 , the initial state, repeated iteration of (1) gives rise to a series of states known as an orbit. An example is the Hénon map, a twodimensional discrete-time nonlinear dynamical system represented by the state equations [Hénon 1976, Alligood et al 1997, Peitgen et al 2004, Kumar 1996, Crutchfield et al 1986, Gleick 1997 …”

Section: The Hénon Mapmentioning

confidence: 99%

Cryptographic pseudo-random sequences from the chaotic Hénon map

Suneel

2009

Sadhana

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A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Hénon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and auto-correlation are investigated. All these properties of the sequences suggest a strong resemblance to random sequences. Results of statistical testing of the sequences are found encouraging. An attempt is made to estimate the keyspace size if the proposed scheme is used for cryptographic applications. The keyspace size is found to be large and is dependent on the precision of the computing platform used.

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Section: The Hénon Mapmentioning

confidence: 99%

Cryptographic pseudo-random sequences from the chaotic Hénon map

Suneel

2009

Sadhana

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“…Finally, one of the characteristics of chaotic systems is that they can be very sensitive to initial conditions, and a slight change in the initial condition can lead to radically different outcomes. Further details can be found in articles and books on the field, e.g., (Crutchfield et al, 1986;Devaney, 1987;Gleick, 1987;Grebogi et al, 1987).…”

Section: Introductionmentioning

confidence: 99%

The induction of dynamical recognizers

Pollack

1991

Mach Learn

183

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Abstract. A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained" on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a "bifurcation" in the limit behavior of the network. This phase transition corresponds to the onset of the network's capacity for generalizing to arbitrary-length strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NP-Hard problem, the architecture does appear capable of generating nonregular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of non-linear dynamical systems.

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“…Rinaldi (1997) suggested that complex systems have four tenents: emergence, self-organization, evolution at the edge of chaos, and the ability to process information. Crutchfield (1986) stated that chaos theory might provide insights into relationships where previously none were thought to exist. Jervis (1997) took this concept a step further in his examination causal relationships and unintended consequences within a system.…”

Section: Disproportionate Effectsmentioning

confidence: 99%

Chaos, complexity, and ethnic conflict: A study in the application of the principles of chaos and complexity theory to the analysis of ethnic conflict

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Chaos

Cited by 387 publications

References 0 publications

Cryptographic pseudo-random sequences from the chaotic Hénon map

Cryptographic pseudo-random sequences from the chaotic Hénon map

The induction of dynamical recognizers

Chaos, complexity, and ethnic conflict: A study in the application of the principles of chaos and complexity theory to the analysis of ethnic conflict

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