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This paper presents experimental switching between two attractors in the swinging bell. In the considered yoke-bell-clapper system, two coexisting solutions appear. In the first one, we observe a single impact between the bell and the clapper per one period of motion, and in the second solution, no impacts occur-no sound is produced. Based on the time-dependent stability margin method, we numerically detect parts of the trajectories where the system is most prone to perturbations. Using this knowledge, we experimentally investigate switching between attractors by applying the perturbation to the clapper. We show that we can easily enforce the change of attractor by properly timing the perturbation. The results prove that, based on the results from the time-dependent stability margin numerical method, we are able to effectively alter the wrong operation of the bell (lack of impact) to the correct operation (solution with impact). The analysis is conducted on the real-world mechanical system rather than paradigmatic examples. Therefore, it contributes to the subject of multistability and nonlinearity in engineering design. Novel, recently developed methods for analyzing multistable systems are successfully employed during the investigation. The paper shows that a complex phenomenon of multistability observed in the system, which is considered simple and undemanding from an engineering design point of view.
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Sample-based methods are a useful tool in analyzing the global behavior of multi-stable systems originating from various branches of science. Classical methods, such as bifurcation diagrams, Lyapunov exponents, and basins of attraction, often fail to analyze complex systems with many coexisting attractors. Thus, we have to apply a different strategy to understand the dynamics of such systems. We can distinguish basin stability, extended basin stability, constrained basin stability, basin entropy, time dependent stability margin, and survivability among sample-based methods. Each method has specific properties and gives us important data about the behavior of the analyzed system. However, none of the methods provides complete information. Hence, to have a full overview of the dynamics, one has to collect data from two or more approaches. This study describes the sample-based methods and presents their advantages and disadvantages for the archetypal nonlinear oscillator with multiple coexisting attractors. Hence, we give helpful information in selecting the best method or methods for analyzing the dynamical system.
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Dinâmica não Linear , EntropiaRESUMO
OBJECTIVES: We aimed at evaluation of the influence of the extent of axillary lymph node dissection, measured by the total number of lymph nodes harvested, on the drainage volume. We also looked at the lymph node positivity (N+) and the number of metastatic axillary lymph nodes as a potential prognostic factors in this regard. MATERIAL AND METHODS: We have analysed the data of 63 patients (F/M: 62/1) with breast cancer who underwent radical modified mastectomy in 2008-2009 in the single department of surgical oncology RESULTS: We observed no significant correlation between the 1) total number of axillary lymph nodes harvested during lymphadenectomy 2) presence of metastatic lymph nodes (node positive disease), 3) number of metastatic axillary lymph nodes and: drainage volume on the day of surgery drainage volume on three consecutive postoperative days and drainage volume from the day of surgery to drain removal. CONCLUSION: The extent of axillary lymph node dissection, measured by the total number of lymph nodes excised, did not influence drainage volume after radical modified mastectomy Neither total number of metastatic lymph nodes excised nor the node positivity (N+) were associated with increased drainage volume after mastectomy with axillary dissection.