Spiral turbulence developed through the formation of superimposed target waves in an oscillatory reaction-diffusion medium

Experimental, numerical, and mechanistic analysis of the nonmonotonic relationship between oscillatory frequency and photointensity for the photosensitive Belousov-Zhabotinsky oscillator

The oscillation frequency of a nonlinear reaction system acts as a key factor for interaction and superposition of spatiotemporal patterns. To control and design spatiotemporal patterns in oscillatory media, it is important to establish the dominant frequency-related mechanism and the effects of external forces and species concentrations on oscillatory frequency. In the Ru(bipy)3(2+)-catalyzed Belousov-Zhabotinsky oscillator, a nonmonotonic relationship exists between light intensity and oscillatory frequency (I-F relationship), which is composed of fast photopromotion and slow photoinhibition regions in the oscillation frequency curve. In this work, we identify the essential mechanistic step of the I-F relationship: the previously proposed photoreaction Ru(II)* + Ru(II) + BrO3(-) + 3H(+) → HBrO2 + 2Ru(III) + H2O, which has both effects of frequency-shortening and frequency-lengthening. The concentrations of species can shift the light intensity that produces the maximum frequency, which we simulate and explain with a mechanistic model. This result will benefit studies of pattern formation and biomimetic movement of oscillating polymer gels.

Diffusion-induced periodic transition between oscillatory modes in amplitude-modulated patterns

We study amplitude-modulated waves, e.g., wave packets in one dimension, overtarget spirals and superspirals in two dimensions, under mixed-mode oscillatory conditions in a three-variable reaction-diffusion model. New transition zones, not seen in the homogeneous system, are found, in which periodic transitions occur between local 1(N-1) and 1(N) oscillations. Amplitude-modulated complex patterns result from periodic transition between (N - 1)-armed and N-armed waves. Spatial recurrence rates provide a useful guide to the stability of these modulated patterns.

Spiral instabilities in media supporting complex oscillations under periodic forcing

The periodically forced Brusselator model displays temporal mixed-mode and quasiperiodic oscillations, period doubling, and chaos. We explore the behavior of such media as reaction-diffusion systems for investigating spiral instabilities. Besides near-core breakup and far-field breakup resulting from unstable modes in the radial direction or Doppler-induced instability (destabilization of the core's location), the observed complex phenomena include backfiring, spiral regeneration, and amplitude modulation from line defects. Amplitude modulation of spirals can evolve to chambered spirals resembling those found in nature, such as pine cones and sunflowers. When the forcing amplitude is increased, the spiral-tip meander evolves from simple rotation to complex petals, corresponding to transformation of the local dynamics from simple oscillations to mixed-mode, period-2, and quasiperiodic oscillations. The number of petals is related to the complexity of the mixed-mode oscillations. Spiral turbulence, standing waves, and homogeneous synchronization permeate the entire system when the forcing amplitude is further increased.

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

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.

Breakup of propagating waves through the development of a transient unexcitable regime

Spontaneous breakup of propagating waves was investigated in this paper with a ferroin-catalyzed Belousov-Zhabotinsky reaction modified with the inclusion of a second substrate, 1,4-cyclohexanedione (CHD). The presence of CHD, which forms a separate chemical oscillator with acidic bromate, led to the development of a scattered unexcitable regime in the studied medium, where as waves passed through these unexcitable media, the propagation was disrupted, causing the creation of free ends. It thus presents a new avenue through which a chemical wave breaks up to form spirals. By manipulating the concentrations of CHD, sulfuric acid, and bromate, unexcitable regimes of different sizes with different survival times were obtained. Kinetic data on wave speed prior to and after the unexcitable window illustrates that the occurrence of an unexcitable regime is not due to depletion of components needed for wave propagation.