Effects of quenched disorder on critical transitions in pattern-forming systems


  Golan Bel [1]  ,  Hezi Yizhaq [1,2]  
[1] Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
[2] The Dead Sea and Arava Science Center, Tamar Regional Council, Israel

Critical transitions are of great interest to scientists in many fields. Most knowledge about these transitions comes from systems exhibiting the multistability of spatially-uniform states. In spatially extended and, particularly, in pattern-forming systems, there are many possible scenarios for transitions between alternative states. Quenched disorder may affect the dynamics, bifurcation diagrams and critical transitions in nonlinear systems. However, only a few studies have explored the effects of quenched disorder on pattern-forming systems, either experimentally or by using theoretical models. Here, we use a well-explored mathematical model describing the dynamics of vegetation in drylands to study the effects of quenched disorder on critical transitions in pattern-forming systems. We find that the disorder affects the pattern formed by introducing an interplay between the imposed pattern and the self-organized one. Moreover, the disorder significantly increases the survivability of the patterned state and makes the transition between the patterned state and the uniform state more gradual.