Generalized multistability and its control in a laser.

We revisit the laser model with cavity loss modulation, from which evidence of chaos and generalized multistability was discovered in 1982. Multistability refers to the coexistence of two or more attractors in nonlinear dynamical systems. Despite its relative simplicity, the adopted model shows us how the multistability depends on the dissipation of the system. The model is then tested under the action of a secondary sinusoidal perturbation, which can remove bistability when a suitable relative phase is chosen. The surviving attractor is the one with less dissipation. This control strategy is particularly useful when one of the competing attractors is a chaotic attractor.

A new chaotic oscillator with free control.

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.