Arm splitting and backfiring of spiral waves in media displaying local mixed-mode oscillations

Abstract

The behavior of spiral waves is investigated in a model of reaction-diffusion media supporting local mixed-mode oscillations for a range of values of a control parameter. This local behavior is accompanied by the formation of nodes, at which the arms of the simple spiral waves begin to split. With further parameter changes, this nodal structure loses stability, becoming quite irregular, eventually evolving into turbulence, while the local dynamics increases in complexity. The breakup of the spiral waves arises from a backfiring instability of the nodes induced by the arm splitting. This process of spiral breakup in the presence of mixed-mode oscillations represents an alternative to previously described scenarios of instability of line defects and superspirals in media with period-doubling and quasiperiodic oscillations, respectively.

Spiral instabilities in media supporting complex oscillations under periodic forcing

“…In excitable and simple oscillatory media, many types of spiral instabilities such as Eckhaus instability, 34,35 Dopplerinduced instability, 36,37 and transverse instability in the presence of a fast-diffusing inhibitor 38 have previously been studied in detail. For media that support complex, e.g., mixed-mode, period-doubling, or quasiperiodic oscillations, such spatial phenomena as line defects, [8][9][10]39 nodes with arm splitting and backfiring, 31 and "overtargets" 40 in spiral evolution have been reported. The former phenomena belong to the class of instabilities of wavelength modulation, whereas the latter results from amplitude modulation.…”