Compensating for imperfections in solvable chaotic oscillators

We show a method to compensate for a class of implementation imperfections in a solvable chaotic oscillator while maintaining an analytic solution. We demonstrate the method by compensating for propagation delay in an electronic circuit realization of the oscillator. The oscillator is a hybrid dynamical system that includes both continuous and discrete states. Implementing the oscillator in hardware is unavoidably imperfect; specifically, switching events in the discrete state are subject to finite slew rates and propagation delays that introduce distortion into the system. The form of the solvable chaotic oscillator enables a compensation method for implementation imperfections that include finite slew rates and propagation delays. Importantly, the resulting compensated system also exhibits an analytic solution. A hardware demonstration of the oscillator operating at 1 MHz closely aligns with the analytic solution. As a result, this study aids high-frequency engineering applications that may benefit from using analytically solvable chaos.