Energy-selective control of noise-assisted multipulsing by weak optical seeding in the dissipative-soliton-resonance regime
We study pulse-number selection in a stochastic cubic--quintic complex Ginzburg--Landau model of a weakly seeded, normal-dispersion laser in the dissipative-soliton-resonance (DSR) regime. Without noise, a single pulse and pulse pairs persist at the same control parameters, and the total energy of an $N$-pulse state follows a ladder constructed from the single-pulse branch. The final energies of noisy trajectories lie close to the same ladder. Multipulsing therefore does not necessarily lose the single-pulse solution. It can reflect which coexisting state the noisy dynamics reaches. Optical seed injection suppresses energy-dependent multipulsing and, at larger seed power, produces a nonmonotonic DSR energy window. An energy--noise scan shows that energy dominates the multipulse probability, whereas additive noise produces only a modest trend common to all energies, without a noise optimum. The noise-induced formation statistics therefore do not establish canonical stochastic resonance or escape from a pre-existing soliton. Coherent control by a weak monochromatic seed extends predominantly single-pulse operation over a noticeably broader energy window, enhancing dissipative-soliton energy scalability. Within an adiabatic approximation, equal energy sharing among coexisting pulses is stable wherever the single-pulse energy grows less than proportionally with the control energy, as it does over the sampled DSR range. Energy exchange between the pulses then relaxes up to about 200 times more slowly than their total energy.