1. What are the contributions in "Control based bifurcation analysis for experiments" ?
The authors introduce a method for tracking nonlinear oscillations and their bifurcations in nonlinear dynamical systems.. Furthermore, the authors track in two parameters the curves of Hopf bifurcation and grazing-sliding bifurcation that form the boundary of the bistability region.
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2. What have the authors stated for future works in "Control based bifurcation analysis for experiments" ?
In the near future the authors are planning to implement their method in prototype substructured experiments, such as mass-springdamper and mass-spring-pendulum systems [ 16 ].. An interesting topic of future research is the continuation of nonperiodic trajectories and their stability changes.. The authors anticipate that the limiting factor to the applicability of continuation methods in a real experiment will be the low accuracy of experimental measurements compared to computer simulations.. When problem specific information is available then the efficiency of the iteration can be increased substantially by incorporating known parts of the linearization into the Jacobian.
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3. What is the common type of nonstationary behavior in nonlinear dynamical systems?
The simplest and most frequently encountered type of self-excited nonstationary behavior in nonlinear dynamical systems are periodic oscillations.
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4. What is the limiting factor to the applicability of continuation methods in a real experiment?
The authors anticipate that the limiting factor to the applicability of continuation methods in a real experiment will be the low accuracy of experimental measurements compared to computer simulations.
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![Fig. 2 Diagram of the experimental results from [12] showing the velocity v versus the amplitude of oscillations. Dots show the amplitude of measured stick-slip oscillations (fitted with a solid curve) and squares refer to measured equilibria. The dashed curve connecting the transitions is the conjectured family (UP) of dynamically unstable periodic orbits. (Reprinted with kind permission from G. Stépán; translations from the Hungarian original courtesy of G. Orosz)](/figures/fig-2-diagram-of-the-experimental-results-from-12-showing-3s0hlvg9.webp)