Parametric generation of robust chaos with time-delayed feedback and modulated pump source

We consider a chaos generator composed of two parametrically coupled oscillators whose natural frequencies differ by factor of two. The system is driven by modulated pump source on the third harmonic of the basic frequency, and on each next period of pumping the excitation of the oscillator of doubled frequency is stimulated by the signal from the oscillator of the basic frequency undergoing quadratic nonlinear transformation and time delay. Using qualitative analysis and numerical results, we argue that chaotic dynamics in the system corresponds to hyperbolic strange attractor. It is a kind of Smale–Williams solenoid embedded in the infinite-dimensional state space of the stroboscopic map of the time-delayed system.

► We propose a scheme of parametric generator of robust chaos. ► Qualitative analysis and numerical simulation data are provided. ► We argue that in the system the hyperbolic attractor of Smale–Williams occurs. ► Advantage is structural stability, insensitivity to parameter variations or noise. ► The scheme may be implemented as electronic or optical device.