Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Hilborn, Robert C.; Sprott, J. C.

doi:10.1119/1.17477

Cited by 115 publications

(162 citation statements)

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“…The emergence of such chaotic behavior can be anticipated based on the analogy to the nonlinear oscillator, [38,[50][51][52] which is well-known to show chaotic behaviors in certain regimes. However, to provide a better understanding of the driving force in the current system, we use finite element methods to compare the energies of the different sub-harmonic modes.…”

Section: 2) Inmentioning

confidence: 99%

The role of substrate pre-stretch in post-wrinkling bifurcations

et al. 2014

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When a stiff film on a soft substrate is compressed, the surface of the film forms wrinkles, with tunable wavelengths and amplitudes that enable a variety of applications. As the compressive strain increases, the film undergoes post-wrinkling bifurcations, leading to period doubling and eventually to formation of localized folds or ridges. Here we study the post-wrinkling bifurcations in films on pre-stretched substrates. Through a combination of experiments and simulations, we demonstrate that pre-stretched substrates not only show substantial shifts in the critical strain for the onset of post-wrinkling bifurcations, but also exhibit qualitatively different post-wrinkled states. In particular, we report on the stabilization of wrinkles in films on pre-tensioned substrates and the emergence of 'chaotic' morphologies in films on pre-compressed substrates.

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Section: 2) Inmentioning

confidence: 99%

The role of substrate pre-stretch in post-wrinkling bifurcations

et al. 2014

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“…4 (cf. e.g., Hilborn, 1994;Jackson, 1989;Jensen et al, 1984). This implies that the stability of a frequency ratio is associated with the width of the attraction regime.…”

Section: Multifrequency Tasksmentioning

confidence: 99%

Dynamical models of movement coordination

Beek

Peper

Stegeman

1995

Human Movement Science

164

107

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This article examines the status of dynamical models of movement coordination qua phenomenological models. After a brief outline of the aims, methods and strategic assump tions of the dynamical systems approach, a survey is provided of the theoretical and empirical progress it has made in identifying general principles of coordination. Although dynamical models are constructed for phenomena at a particular level of analysis for which they provide descriptive explanations, their dynamics can sometimes he linked to or associated with the dynamics of processes at other levels of analysis. The article concludcs with a tentative scheme to clarify the position of the dynamical approach relative to other ex! an I approaches in movement science, « W ipBodily movements occur in the context of the everyday functioning of people while realizing specific task goals. As a rule, such movements involve the participation of multiple joints and limbs. When in action, these body parts are coordinated, that is, they are brought into proper relation to one another as well as to the surrounding layout of surfaces (cf. Turvey, 1990). To the naked eye, this coordination may look relatively simple, as in picking up an object, or relatively complicated, as in juggling, performing an attacking forehand drive in table tennis or playing the drums. To the ( 'orrcspoiKling author. Tel.: +31 20 444 8532. Fax: +31 20 444 5867. E-mail: 1' .1 HeekWl'BW .VU.NL (l|li7-lM 5 7 /l)5/$(W.50 < v> 1W5 I Use vier Science U.V. A ll lights reserved S S D I 0 I ()7-t) 4 5 7 ( t>5 MI0028-3 movement scientist, however, all coordination is complex in that he or she is confronted with the challenge to explain coordinated movements as the orderly products of a hybrid biological organization involving a very large number of different subsystems (e.g., vascular, neural, muscular, skeletal). These subsystems are operating at different rates and are connected in intricate ways. Due to this compositional complexity, the problem of movement coordination is extremely difficult to resolve in a scientifically satisfactory way. Finding an adequate solution is hampered by the fact that the field of motor control is still very much partitioned according to the traditional disciplines of movement science (mechanics, neuropliysiology, psychology, and so on), whereas a multidisciplinary or interdisciplinary approach is required.Broadly speaking, two types of approaches may be distinguished in movement science: structural and phenomenological approaches (ef, Otten, 1991). Structural approaches seek causal explanations of movement in terms of dedicated structures within the human body. Phenomenological approaches, in contrast, seek noncausal explanations in terms of phe nomenological laws and principles without reference to dedicated mecha nisms and structures within the human body.Structural models of motor control are typically (neuro)physiological models which attempt to explain different aspects of motor behaviour on the basis of hypothetical (neuro)physiologieal m...

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“…Among the wealth of phenomena displayed by nonlinear systems maintained far from thermodynamic equilibrium, [1][2][3][4] perhaps the most remarkable are deterministic chaos and the scenarios by which it evolves from simple oscillations. These "universal" behaviors appear in a variety of systems in physics, engineering, biology, chemistry, and electrochemistry.…”

Section: Introductionmentioning

confidence: 99%

“…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. 1 In these scenarios, the system first undergoes a Hopf bifurcation, which generates a stable limit cycle from a steady state. As the control parameter is further varied, an additional fundamental frequency can arise, causing more complex oscillations.…”

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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Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Cited by 115 publications

References 0 publications

The role of substrate pre-stretch in post-wrinkling bifurcations

The role of substrate pre-stretch in post-wrinkling bifurcations

Dynamical models of movement coordination

Dynamic Complexity in the Electrochemical Oxidation of Thiourea

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