On attractors and stability for semigroup actions and control systems

Souza, Josiney A.; Barros, Carlos J. Braga; Rocha, Victor H. L.

doi:10.1002/mana.201400389

Cited by 5 publications

(5 citation statements)

References 15 publications

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“…The central tenet of this work is that the phase portrait trajectories of fingertip forces—as quantified by their reconstructed attractors—are informative of neuromuscular control to stabilize the unstable spring-hand system. As discussed in, for example [ 36 , 37 ], there are strong relations among the various notions of attractors and stability for dynamical systems. Therefore, detecting an attractor in the phase portrait of our manipulation task at the edge of instability—as our results show—is indicative of a stabilizing action by the neuro-musculo-skeletal system.…”

Section: Discussionmentioning

confidence: 99%

Characterization of the disruption of neural control strategies for dynamic fingertip forces from attractor reconstruction

et al. 2017

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The Strength-Dexterity (SD) test measures the ability of the pulps of the thumb and index finger to compress a compliant and slender spring prone to buckling at low forces (<3N). We know that factors such as aging and neurodegenerative conditions bring deteriorating physiological changes (e.g., at the level of motor cortex, cerebellum, and basal ganglia), which lead to an overall loss of dexterous ability. However, little is known about how these changes reflect upon the dynamics of the underlying biological system. The spring-hand system exhibits nonlinear dynamical behavior and here we characterize the dynamical behavior of the phase portraits using attractor reconstruction. Thirty participants performed the SD test: 10 young adults, 10 older adults, and 10 older adults with Parkinson’s disease (PD). We used delayed embedding of the applied force to reconstruct its attractor. We characterized the distribution of points of the phase portraits by their density (number of distant points and interquartile range) and geometric features (trajectory length and size). We find phase portraits from older adults exhibit more distant points (p = 0.028) than young adults and participants with PD have larger interquartile ranges (p = 0.001), trajectory lengths (p = 0.005), and size (p = 0.003) than their healthy counterparts. The increased size of the phase portraits with healthy aging suggests a change in the dynamical properties of the system, which may represent a weakening of the neural control strategy. In contrast, the distortion of the attractor in PD suggests a fundamental change in the underlying biological system, and disruption of the neural control strategy. This ability to detect differences in the biological mechanisms of dexterity in healthy and pathological aging provides a simple means to assess their disruption in neurodegenerative conditions and justifies further studies to understand the link with the physiological changes.

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Section: Discussionmentioning

confidence: 99%

Characterization of the disruption of neural control strategies for dynamic fingertip forces from attractor reconstruction

et al. 2017

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“…In this paper, we follow the nomenclature of [18] and use the term Conley for attractors of Conley's theory to distinguish the attractors of the classical theory of dynamical systems (see [1,2]) from the attractors of Conley's theory.…”

Section: Control Systemsmentioning

confidence: 99%

“…In this paper, we apply the results obtained in [18] to relate these concepts for control systems on vector bundles. Since the dynamics of the class of control systems considered in this paper is given by means of the action of the semigroup of the system, we can apply here the results of the general theory of semigroup actions.…”

Section: Introductionmentioning

confidence: 97%

“…In [18], Braga Barros, Souza and Rocha present results on the relation among Conley attractors, attractors and Lyapunov stable sets for semigroup actions and control systems. In this paper, we apply the results obtained in [18] to relate these concepts for control systems on vector bundles.…”

Section: Introductionmentioning

confidence: 99%

“…Here, the translation hypotheses (see Definition 2.1), especially the hypotheses called H 3 and H 4 , are fundamental. These hypotheses have been used in the literature to study the asymptotic behavior of semigroup actions and control systems (for instance, see [13,14,19,15,17,18,[20][21][22]). The hypothesis H 3 yields a relation among the concepts of stable weak attractor, attractor, uniform attractor, stable set and asymptotic stable set (see Proposition 2.2), while the hypothesis H 4 yields invariance for the ω-limit sets (see Proposition 2.1), which is fundamental in Lemma 3.1.…”

Section: Introductionmentioning

confidence: 99%

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