Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours

Bifurcation scenarios, dynamical integrity and control of noncontact atomic force microscopes

The research focuses on the description of the global dynamical behavior of a reduced-order model of noncontact Atomic Force Microscope. Different numerical analyses and continuation techniques are carried out to investigate the evolution of the main system periodic solutions and relevant basins of attraction under variations of the most significant system parameters. Local bifurcations, stability boundaries and basin erosion processes around primary and subharmonic resonance regions are studied in presence of both the parametrical horizontal excitation and the external one, and the obtained behavior charts are used not only to compare the results with the literature ones, but also as practical instruments to characterize the operation ranges in terms of the selected parameters. With the same perspective, dynamical integrity concepts, such as detection of basins of attraction, and quantification of their erosion process via integrity measures, are applied to determine acceptable frequency-dependent thresholds associated with a priori safe design targets. Furthermore, an external feedback control is introduced with the aim to take the system response to a selected reference one, thus providing a simple and efficient method to avoid possible unstable motions. Upon checking the effectiveness of the procedure in the weakly nonlinear regime via a perturbation approach, several numerical analyses in the strongly nonlinear regime are accomplished to achieve a description of its dynamical behavior as a function of the newly inserted parameters, and to critically evaluate the effectiveness of the control actuation on the system dynamics, with also a view to the overall response scenario