Robust Hyperbolic Chaos in Froude Pendulum with Delayed Feedback and Periodic Braking

We indicate a possibility of implementing hyperbolic chaos using a Froude pendulum that is able to produce self-oscillations due to the suspension on a shaft rotating at constant angular velocity, in the presence of time-delay feedback and of periodic braking by the application of additional frictional force. We formulate a mathematical model and carry out its numerical research. In the parameter space we reveal areas of chaotic and regular dynamics using the analysis of Lyapunov exponents and some other diagnostic tools. It is shown that there are regions in the parameter space where the Poincaré stroboscopic map has an attractor, which is a kind of Smale–Williams solenoid embedded in the infinite-dimensional state space. We confirm the hyperbolicity of the attractor by numerical calculations including the analysis of angles of intersections of stable and unstable invariant subspaces of vectors of small perturbations for trajectories on the attractor and verify the absence of tangencies between these subspaces.

Hyperbolic Chaos and Other Phenomena of Complex Dynamics Depending on Parameters in a Nonautonomous System of Two Alternately Activated Oscillators

We provide a multiparameter analysis of dynamics in a nonautonomous system of two alternately exciting self-oscillatory elements that are able to demonstrate a uniformly chaotic attractor of Smale–Williams type in the stroboscopic Poincaré map. Parameter space charts of regular and chaotic regimes are presented. Possible scenarios of the onset of hyperbolic chaos are discussed. The numerical studies are supplemented by experimental results obtained for a laboratory electronic device.