Controlling chaos to store information in time-delayed feedback systems

Nonlinear delay-differential equations (DDE´s) commonly appear in models of physiological and neural control. In certain parameter ranges, for example in chaotic regimes, such equations have unstable periodic orbits (UPO´s). Furthermore, these equations exhibit multistability when the delay to response time ratio is significantly greater than one. We first show that the UPO´s can be stabilized using a second delayed feedback control. We then show that the controlled solutions are multistable. This enables us to encode a finite string of bits into a particular waveform of an unstable periodic solution. Our results indicate that it is possible to control the time evolution of DDE´s using appropriate initial functions