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 waves are ubiquitous in nonlinear science, appearing in a wide range of biological, chemical, and physical systems. In many systems, simple spirals evolve into more complex structures, and several scenarios have been identified by which this process can take place. Often, formation of complex spiral structures leads to spiral breakup and spiral turbulence. Again, generic scenarios by which this behavior emerges have been studied. In this paper, we identify through the numerical investigation of a model of two coupled allosteric enzymes a novel mechanism, characterized by the splitting of spiral arms, that produces complex spiral waves, which can subsequently evolve into spiral turbulence via a distinctive breakup process involving collision of waves with backfired segments expelled by their neighbors.