Cavity solitons, appearing in the transverse plane of nonlinear optical cavities, have been advocated for use in fast and compact optical information storage. Localized structures may develop a number of instabilities like start moving, breathing, or oscillating. In the latter case, they would oscillate in time while remaining stationary in space. The Lugiato-Lefever Kerr model shows a route in which autonomous oscillating cavity solitons are destroyed, leading to an excitability regime. Excitability is a concept arising originally from biology (e.g., neuroscience), and it has been found in a variety of systems, including optical systems. Typically a system is said to be excitable if while it sits at a stable fixed point, perturbations beyond a certain threshold induce a large response before coming back to the rest state Here we introduce an addressing beam which allow us to control the properties of this excitability. The presence of this addressing beam introduces a new route to excitability with a tunable threshold. We also study the interaction of two cavity solitons, both in the oscillatory and in the excitable regimes. Finally we study the effect of noise in the system and the possibility of coherence resonance.
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