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Dr. Golan Bel,Ben-Gurion University of the Negev | The Racah Institute of Physics

Dr. Golan Bel,Ben-Gurion University of the Negev

Date: 
Wed, 11/12/201312:00-13:30
Location: 
Danciger B building, Seminar room
"Critical and gradual transitions in pattern forming systems":
Critical transitions have attracted a great deal of attention due to their relevance to many natural and social systems. Much research has been devoted to the characterization and identification of imminent critical transitions. In spatially extended systems, the dynamics (near and away from the critical point) is more complicated due to the expansion, shrinking and coalescence of alternative-state domains. Pattern-forming systems introduce additional complexity due to the patterned nature of one of the stable states.
In this talk, I will present several works in which we used the context of drylands vegetation dynamics to study various aspects of this additional complexity. We studied the interplay of two distinct pattern-forming mechanisms leading to the same type of instability. We found that the co-occurrence of such instabilities results in the growth of a single mode rather than two interacting modes. The interplay between the two mechanisms, which promote or counteract each other, compensates for the simpler dynamics of a single mode by inducing higher pattern diversity. Using a minimal model, we showed that in systems exhibiting a bistability of patterned state with a uniform state, a multitude of intermediate stable localized states may appear, giving rise to step-like gradual shifts with extended pauses at these states. This result suggests that a combination of abrupt-shift indicators and gradual-shift indicators might be needed to unambiguously identify regime shifts. The existence of these localized states in models for the dynamics of drylands vegetation and the response of the systems described by these models to local perturbations will be discussed. We showed how a simplified version of a model for drylands vegetation dynamics can explain the emergence and the observed dynamics of the spectacular phenomenon of “fairy circles” in southern Africa.
If time permits, I will present recent results demonstrating the effects of quenched disorder on the pattern formation, survivability and resilience of water-limited vegetation.