English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the Yamada model for an excitable or self-pulsating laser withsaturable absorber, and study the effects of delayed optical self-feedback inthe excitable case. More specifically, we are concerned with the generation ofstable periodic pulse trains via repeated self-excitation after passage throughthe delayed feedback loop, as well as their bifurcations. We show that onsetand termination of such pulse trains correspond to the simultaneous bifurcationof countably many fold periodic orbits with infinite period in this delaydifferential equation. We employ numerical continuation and the concept ofreappearance of periodic solutions to show that these bifurcations coincidewith codimension-two points along families of connecting orbits and foldperiodic orbits in a related advanced differential equation. These pointsinclude heteroclinic connections between steady states, as well as homoclinicbifurcations with non-hyperbolic equilibria. Tracking these codimension-twopoints in parameter space reveals the critical parameter values for theexistence of periodic pulse trains. We use the recently developed theory oftemporal dissipative solitons to infer necessary conditions for the stabilityof such pulse trains.

The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback