No abstract

In this work we carry out extensive numerical study of a Watt-centrifugal-governor system model, and we also implement an electronic circuit by analog computation to experimentally solve the model. Our numerical results show the existence of self-organized stable periodic structures (SPSs) on parameter-space of the largest Lyapunov exponent and isospikes of time series of the Watt governor system model. A peculiar hierarchical organization and period-adding bifurcation cascade of the SPSs are observed, and this self-organized cascade accumulates on a periodic boundary. It is also shown that the periods of these structures organize themselves obeying the solutions of Diophantine equations. In addition, an experimental setup is implemented by a circuitry analogy of mechanical systems using analog computing technique to characterize the robustness of our numerical results. After applying an active control of chaos in the experiment, the effect of intrinsic experimental noise was minimized such that, the experimental results are in astonishing well agreement with our numerical findings. We can also mention as another remarkable result, the application of analog computing technique to perform an experimental circuitry analysis in real mechanical problems.

In this work we carry out experimental studies of the paradigmatic Chua's circuit using an approach of the analog computation instead of performing experiments in the canonical circuit. This means that we have built an electronic circuit that integrates (analog computation), in continuous time, the equations of motion of the canonical Chua's circuit. The equations of motion of the analogical circuit are equivalent to the canonical circuit, so that the dynamical behaviour is the same. With this approach, we successfully obtain an experimental parameter plane using the largest Lyapunov exponent (here named Lyapunov diagram), directly calculated from the experimental time series, with a good precision, so that different types of dynamical behaviours were characterized in this diagram. Results are in very good agreement with numerical simulation with an additional Gaussian noise. The approach by analog computation used here can be extended to a wide range of dynamical systems, once that the analog circuit simulates, by circuitry implementation, the dynamics of these systems from an experimental point of view.

No abstract

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show that for tiny harmonic perturbations only the smallest stable periodic structures (SPSs) immersed in chaotic domains are destroyed, whereas for intermediate harmonic perturbation amplitudes there is the emergence of quasiperiodic motion, with the existence of typical Arnold tongues and, the consequent distortion of the SPSs embedded in the chaotic region. For large enough harmonic perturbations, the SPSs immersed in chaotic domains are suppressed and the dynamics becomes essentially chaotic. Regarding the noise perturbations, it is able to suppress periodic motion even if tiny noise intensities are considered, as analyzed by a periodic attractor subject to different noise intensities. The threshold of noise amplitude for chaos generation in periodic structures is reported by both methods. Additionally, we investigate the robustness of the 0-1 test for chaos characterization in both noiseless and noise cases, and for the first time, we compare the Lyapunov exponents and 0-1 test methods in the parameter-planes. Our findings are generic due to their remarkable agreement with results previously reported for dynamical systems in other contexts.