Bifurcations and Crises in a Shape Memory Oscillator

Machado, Luciano; Savi, Marcelo A.; Janeiro, Rio de

doi:10.1155/2004/717986

Cited by 24 publications

(8 citation statements)

References 29 publications

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“…Bifurcation diagrams represent the stroboscopically sampled variable values under the slow quasi-static increase of some system parameter (Thompsom & Stewart, 1986). These diagrams allow a global analysis of the parameter changes in the system response (Machado et al, 2004). Figure 12 shows some typical bifurcation diagrams obtained from the logistic map.…”

Section: Bifurcationsmentioning

confidence: 99%

Chaos and order in biomedical rhythms

Savi

2005

J. Braz. Soc. Mech. Sci. & Eng.

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Nature is full of nonlinearities, responsible for a great variety of responses in natural systems. Physiological rhythms constitute a central characteristic of life, which is motivating the analysis of dynamical aspects related to natural systems. Natural rhythms could be either periodic or irregular over time and space and, each kind of dynamical behavior may be related to both normal and pathological physiological functioning. This review article presents an overview of nonlinear dynamics and chaos concepts useful for the analysis of biomedical system. After that, it is presented an overview of dynamical aspects related to different biomedical systems. Cardiovascular rhythms, brain rhythms, cellular and molecular rhythms are discussed from a dynamical approach pointing some characteristics of normal and pathological responses

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Section: Bifurcationsmentioning

confidence: 99%

Chaos and order in biomedical rhythms

Savi

2005

J. Braz. Soc. Mech. Sci. & Eng.

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“…Several references have numerically investigated the complex dynamic response of SMA systems, including the possibility of chaotic responses. 2,[6][7][8][9][10][11][12][13] This work discusses the dynamical response of SMA system considering a 1-DOF oscillator, where the restitution force is provided by a pseudoelastic SMA element. A thermomechanical constitutive model built upon the Boyd and Lagoudas model 14, 15 is used to simulate the SMA constitutive behavior.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics and chaos in a shape memory alloy pseudoelastic oscillator

2007

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Shape memory alloys (SMAs) have been used in different kind of application including those that explore their dynamical response. The key characteristics of SMAs are associated with adaptive dissipation related to their hysteretic behavior and changes in their material properties caused by martensitic phase transformations. This work discusses the dynamical response of one-degree of freedom (1-DOF) oscillator where the restitution force is provided by an SMA pseudoelastic element described by a smooth constitutive model built upon the BoydLagoudas model. Numerical simulations show a very intricate dynamic response of the system, with even chaotic responses. Nonlinear tools are employed to determine the nature of the system motion and Lyapunov exponents are used to assure conclusions concerning chaotic behavior.

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“…When employed in dynamical systems, superelastic SMA elements may induce non-regular chaotic responses, as shown for example in [3][4][5][6][7][8][9][10][11]. The eventual presence of such chaotic motions may be an important aspect considered in the design of application and, for this reason, it is very important to be able to detect them.…”

Section: Introductionmentioning

confidence: 99%

Recurrence analysis of regular and chaotic motions of a superelastic shape memory oscillator

et al. 2017

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Abstract. The recurrence analysis is a promising tool for diagnostics of periodic and chaotic solutions, as well as identifying bifurcations. This paper deals with the application of this analysis for the first time to identify regular and non-regular motions of a superelastic shape memory alloy oscillator. The numerical analyses show that the method is capable of distinguishing periodic and chaotic trajectories. Recurrence quantities are applied, showing that different approaches are possible to establish the distinction between periodic and chaotic signals. Basically, recurrence entropy, trapping time, and characteristic recurrence time are considered.

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Bifurcations and Crises in a Shape Memory Oscillator

Cited by 24 publications

References 29 publications

Chaos and order in biomedical rhythms

Chaos and order in biomedical rhythms

Nonlinear dynamics and chaos in a shape memory alloy pseudoelastic oscillator

Recurrence analysis of regular and chaotic motions of a superelastic shape memory oscillator

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