Effect of a variable delay in delayed dynamical systems

We report numerical evidence of the effects of a periodic modulation in the delay time of a delayed dynamical system. By referring to a Mackey-Glass equation and by adding a modula- tion in the delay time, we describe how the solution of the system passes from being chaotic to shadow periodic states. We analyze this transition for both sinusoidal and sawtooth wave mod- ulations, and we give, in the latter case, the relationship between the period of the shadowed orbit and the amplitude of the modulation. Future goals and open questions are highlighted.

Noise-induced attractor annihilation in the delayed feedback logistic map

We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.

Periodic time-domain modulation for the electrically tunable control of optical pulse train envelope and repetition rate multiplication

An electrically tunable system for the control of optical pulse sequences is proposed and demonstrated. It is based on the use of an electrooptic modulator for periodic phase modulation followed by a dispersive device to obtain the temporal Talbot effect. The proposed configuration allows for repetition rate multiplication with different multiplication factors and with the simultaneous control of the pulse train envelope by simply changing the electrical signal driving the modulator. Simulated and experimental results for an input optical pulse train of 10 GHz are shown for different multiplication factors and envelope shapes.