Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials
arXiv:0810.2808 · doi:10.1103/PhysRevA.77.033841
Abstract
In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced Gelens et al., Phys. Rev. A 75, 063812 2007 generalization of the Lugiato-Lefever model that includes a weakly nonlocal response of an intracavity metamaterial. A rich scenario, in which the localized structures exhibit different types of oscillatory instabilities, tristability, and excitability, including a regime of conditional excitability in which the system is bistable, is presented and discussed. Finally, it is shown that the scenario is organized by a pair of Takens-Bogdanov codimension-2 points.
8 pages, 9 figures
References in corpus (6)
- Complex Patterns in a Simple System
- Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials
- Excitability mediated by localized structures
- Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures
- Localized states in bistable pattern forming systems
- Phase-space structure of two-dimensional excitable localized structures
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