Generalized Haus master equation model for mode-locked class-B lasers.

Using an asymptotic technique, we develop a generalized version of the class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power.

Topological characterization of deterministic chaos: enforcing orientation preservation.

The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems.

Stability of square oscillations in a delayed-feedback system.

A semianalytical theory of the stability of odd-harmonic square oscillation modes of a nonlinear delayed-feedback system operating in the period-2 regime is proposed. Stability is found to be ruled by how the system approaches or leaves plateaus. An organization of the stability domains in interrupted bands of values of the delay is revealed.