<i>From Clocks to Chaos: The Rhythms of Life</i>

Glass, Leon; Mackey, Michael C.; Zweifel, P. F.

doi:10.1063/1.2811091

Cited by 447 publications

(437 citation statements)

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“…The SWIFT model is a (stochastic) nonlinear dynamical system with time delay, a class of models that can generate very rich behavior (Glass & Mackey, 1988). Although the complexity of behavior generated by our model is qualitatively as rich as the experimentally observed eye movements, the mathematical analysis of model simulations provides new insight into the underlying principles of eye-movement control.…”

Section: Appendix C Dynamical Analysis Of Swiftmentioning

confidence: 98%

SWIFT: A Dynamical Model of Saccade Generation During Reading.

Engbert

Nuthmann

Richter

et al. 2005

Psychological Review

923

1,071

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Mathematical models have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (R. Engbert, A. Longtin, & R. Kliegl, 2002) were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements observed in reading experiments. The authors present an advanced version of SWIFT that integrates properties of the oculomotor system and effects of word recognition to explain many of the experimental phenomena faced in reading research. They propose new procedures for the estimation of model parameters and for the test of the model's performance. They also present a mathematical analysis of the dynamics of the SWIFT model. Finally, within this framework, they present an analysis of the transition from parallel to serial processing.In modern society, reading is a central skill, which demonstrates how efficiently a range of different cognitive processes (e.g., visual information processing, word recognition, attention, oculomotor control) can work together to perform a complex everyday task. Consequently, a full account of how we read is among the crucial problems of cognitive research. Here, we focus on the fact that eye movements in reading represent an important example for a coupled cognitive-motor system. Therefore, a detailed analysis of the interface between high-level cognition (word recognition) and eye-movement control (saccade generation) is essential to contribute to our knowledge of reading.The measurement, analysis, and modeling of eye movements is one of the most powerful approaches to studying the way visual information is (a) processed by the human mind and (b) used to guide our actions (Findlay & Gilchrist, 2003). Measurements of fixation durations on words or on regions of text are central for investigating cognitive processes underlying reading (Liversedge & Findlay, 2000;Rayner, 1998). Therefore, it is of central importance to develop a detailed understanding of how the experimental observables are related to the underlying cognitive systems.Over the last decades, there has been a considerable increase of knowledge about eye movements and visual information processing (e.g., Hyönä, Radach, & Deubel, 2003; Radach, Kennedy, & Rayner, 2004;Rayner, 1998). The question of how the contributing cognitive subsystems for a specific task such as reading are coordinated is a research problem representative of questions that we believe cannot be investigated without fully quantitative mathematical models. Although it is still possible to investigate aspects of eye-movement control (e.g., word skipping or programming of refixations) in a nonmathematical way, a fully quantitative approach in which most of the experimental phenomena are integrated is necessary to test the interaction of different theoretical assumptions (e.g., the potential impact of a mechanism for word skipping on refixation behavior). In perspective, computational models can be approximated with ...

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Section: Appendix C Dynamical Analysis Of Swiftmentioning

confidence: 98%

SWIFT: A Dynamical Model of Saccade Generation During Reading.

Engbert

Nuthmann

Richter

et al. 2005

Psychological Review

923

1,071

View full text Add to dashboard Cite

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“…Although we consider only one preparatory action potential, our model is so simple that identical results would be obtained from multiple preparatory action potentials. Experimental data from this protocol is often fitted with a restitution function of the form [e.g., Nolasco and Dahlen (1968), Guevara et al (1984), Glass and Mackey (1988)]…”

Section: Remarkmentioning

confidence: 99%

A two-current model for the dynamics of cardiac membrane

Mitchell

Schaeffer

2003

Bulletin of Mathematical Biology

293

318

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In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon-subcritical alternansthat does not occur for the commonly used exponential map.

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“…These "universal" behaviors appear in a variety of systems in physics, engineering, biology, chemistry, and electrochemistry. [5][6][7][8][9][10][11][12][13][14] The effort to understand chaos has attracted a great deal of attention in the past four decades. When a parameter of a deterministic system is varied, chaotic behavior can appear through a number of routes, including period-doubling, quasiperiodic, mixed-mode, and intermittent bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Complexity in the Electrochemical Oxidation of Thiourea

Feng

Gao

et al. 2008

J. Phys. Chem. A

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We explored the temperature-dependent dynamics of the electrochemical oxidation of thiourea under potentialcontrol mode and found complex oscillations with one large peak and one small peak per period. Adjusting the temperature caused the relative amplitudes and positions of the two peaks to vary. Experiments showed that there were two distinct oscillatory regimes as a function of the external current, and at some temperatures, three-frequency quasiperiodic oscillations occurred for current densities between the two oscillatory windows. We examined the species present and the component reactions by employing cyclic voltammetry and electrolysis-HPLC-MS in the two oscillatory regimes. Adsorption and desorption of multiple species, including water and chloride, contribute to the rich dynamical phenomena that were observed.

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From Clocks to Chaos: The Rhythms of Life

Cited by 447 publications

References 0 publications

SWIFT: A Dynamical Model of Saccade Generation During Reading.

SWIFT: A Dynamical Model of Saccade Generation During Reading.

A two-current model for the dynamics of cardiac membrane

Dynamic Complexity in the Electrochemical Oxidation of Thiourea

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