Localized pattern formation in tristable driven dissipative systems
Localized structures (LSs) are fascinating patterns emerging in systems far from thermodynamic equilibrium. Examples include cavity solitons in nonlinear optical cavities, oscillons in granular media, fairy circles in semi-arid regions, and morning glory clouds.
In one-dimensional systems, LS formation generally relies on bistability and front pinning [Int. J. Bifurc. Chaos 12, 2445 (2002)]. Two main scenarios occur: coexistence of two uniform states, producing LSs described by collapsed homoclinic snaking [Physica D 206, 82 (2005)], and coexistence of a uniform state with a periodic pattern through a subcritical Turing bifurcation, leading to standard homoclinic snaking [Physica D 129, 147 (1999)].
When both scenarios coexist, the system becomes tristable, allowing an extraordinary variety of LS configurations and complex bifurcation structures involving hybrid states [SIAM J. Appl. Dyn. Syst. 22, 2693–2731 (2023)].
In this seminar, I will present a complete analysis of such transition utilizing the Swift-Hohenberg equation, a prototypical model generally used in the study of spatiotemporal pattern formation across different disciplines. I will show that the transition between these scenarios is organized through a sequence of necking bifurcations. Moreover, to confirm the generality of this transition, similar analysis in other domains of nonlinear science, such as nonlinear optics and in reaction-diffusion systems, is presented.
This IFISC Seminar will be broadcasted in the following zoom link: https://us06web.zoom.us/j/89466064429?pwd=po9p99eAEYVPaNI8xIIGoOIz0hOqaF.1
Coffee and cookies will be served 15 minutes before the start of the seminar
Contact details:
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