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

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Title: Implications of tristability on localization phenomena: A necking bifurcation's tale.
Authors: Akakpo, Edem Kossi1 (AUTHOR), Haelterman, Marc1 (AUTHOR), Leo, Francois1 (AUTHOR), Parra-Rivas, Pedro1,2 (AUTHOR) pedro.parra-rivas@uniroma1.it
Source: Chaos, Solitons & Fractals. Sep2024, Vol. 186, pN.PAG-N.PAG. 1p.
Subjects: Snakes
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. • Our work investigates the formation of localized dissipative structures in extended tristable systems. • We report a complex, but smooth, transition between standard- homoclinic-snaking- and collapsed-homoclinic-snaking-related localized states. • This transition is mediated by a cascade of necking bifurcations which organize the parameter space of these types of systems. • Our results confirm that this transition is universal in uniform-pattern-uniform tristable systems. [ABSTRACT FROM AUTHOR]
Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Implications of tristability on localization phenomena: A necking bifurcation's tale.
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  Data: 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. • Our work investigates the formation of localized dissipative structures in extended tristable systems. • We report a complex, but smooth, transition between standard- homoclinic-snaking- and collapsed-homoclinic-snaking-related localized states. • This transition is mediated by a cascade of necking bifurcations which organize the parameter space of these types of systems. • Our results confirm that this transition is universal in uniform-pattern-uniform tristable systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.chaos.2024.115201
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      – Code: eng
        Text: English
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      – TitleFull: Implications of tristability on localization phenomena: A necking bifurcation's tale.
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            – D: 01
              M: 09
              Text: Sep2024
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              Y: 2024
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              Value: 186
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