Abstract
This work investigates the existence and bifurcation structure of multi-pulse steady-state solutions to bistable lattice dynamical systems. Such solutions are characterized by multiple compact disconnected regions where the solution resembles one of the bistable states and resembles another trivial bistable state outside of these compact sets. It is shown that the bifurcation curves of these multi-pulse solutions lie along closed and bounded curves (isolas), even when single-pulse solutions lie along unbounded curves. These results are applied to a discrete Nagumo differential equation and we show that the hypotheses of this work can be confirmed analytically near the anti-continuum limit. Results are demonstrated with a number of numerical investigations.
Publisher
Cambridge University Press (CUP)
Reference43 articles.
1. Isolas Versus Snaking of Localized Rolls
2. Patterns and localized structures in bistable semiconductor resonators
3. Geometric localization in supported elastic struts;Michaels;P. Roy. Soc. A-Math. Phy,2019
4. Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities;Yulin;Discret. Contin. Dyn. S,2011
5. Exponential asymptotics of localised patterns and snaking bifurcation diagrams
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献