Turbulence and standing waves in oscillatory chemical reactions with global coupling

Abstract

Using the model of the complex Ginzburg–Landau equation with global coupling, the influence of long-range interactions on the turbulent state of oscillatory reaction–diffusion systems is investigated. Experimental realizations of such a system are, e.g., oscillatory reactions on single crystal surfaces where some of the phenomena we simulate have been observed experimentally. We find that strong global coupling suppresses turbulence by transforming it into a pattern of standing waves or into uniform oscillations. Weaker global coupling gives rise to an intermittent turbulent state which retains partial synchrony.

Emergence and transitions of dynamic patterns of thickness oscillation of the plasmodium of the true slime mold Physarum polycephalum

“…4 and 5). Generally, a standing wave is difficult to explain in terms of a coupled oscillator model with simple local coupling, and the introduction of a negative long-range coupling, which causes wave instability, is successful in demonstrating standing waves [35][36][37][38][39][40]. This mechanism seems plausible in the Physarum plasmodium, because the thickness oscillations between distant parts interact chemically and mechanically via protoplasmic flow [11,14,41].…”

Chemical waves and localized chaos in a model of heterogeneous catalytic reaction in a porous particles

“…The global gaseous-phase linkage has been studied in an abstract model described by the Ginzburg-Landau equation. In the one-dimensional case, a strong global linkage synchronizes the local oscillators [4,5]. As the strength of the linkage diminishes, the model produces standing waves and turbulence.…”

Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering

“…For example, in gas-solid systems mixing in the gas phase produces a global coupling because a consumption of reactants or production of products at one location causes changes in conditions at all locations of the system. 21 Such coupling can have a strong role in altering pattern formation. 22 In electrochemical systems a nonlocal coupling among reactive sites arises through the electric field; potential changes at some location are transmitted rapidly to other locations.…”