Implications of tristability on localization phenomena: a necking bifurcation's tale
arxiv(2024)
摘要
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.
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