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Implications of tristability on localization phenomena: A necking bifurcation’s tale

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  • Akakpo, Edem Kossi
  • Haelterman, Marc
  • Leo, Francois
  • Parra-Rivas, Pedro

Abstract

We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended states. In the tristable regime investigated here two extended uniform states coexist with one periodic Turing pattern. This scenario leads to the transition from the standard-homoclinic-snaking-related localized states associated with uniform-pattern bistability to the collapsed-homoclinic-snaking-related states which arise in a uniform-bistable configuration. We find that this transition is mediated by the emergence of hybrid states through codimension-two necking bifurcations. To perform this study we use bifurcation analysis on a non-variational mean-field model describing the spatiotemporal dynamics of light pulses in passive Kerr cavities.

Suggested Citation

  • Akakpo, Edem Kossi & Haelterman, Marc & Leo, Francois & Parra-Rivas, Pedro, 2024. "Implications of tristability on localization phenomena: A necking bifurcation’s tale," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007537
    DOI: 10.1016/j.chaos.2024.115201
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    1. Maxwell Rowley & Pierre-Henry Hanzard & Antonio Cutrona & Hualong Bao & Sai T. Chu & Brent E. Little & Roberto Morandotti & David J. Moss & Gian-Luca Oppo & Juan Sebastian Totero Gongora & Marco Pecci, 2022. "Self-emergence of robust solitons in a microcavity," Nature, Nature, vol. 608(7922), pages 303-309, August.
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