Front explosion in a periodically forced surface reaction

Pattern formation in reaction-diffusion systems in the presence of non-Markovian diffusion

We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatiotemporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to use reductive perturbation to investigate the formation and stability of patterns. Focusing in detail on the Hopf instability and short-term memory, we derive the corresponding complex Ginzburg-Landau equation that governs the amplitude of the critical mode and we establish the explicit dependence of its parameters on the memory properties. Numerical solution of this memory-dependent complex Ginzburg-Landau equation as well as direct numerical simulation of the non-Markovian Brusselator model illustrates that memory changes the properties of the spatiotemporal patterns. Our results indicate that going beyond the Markovian approximation might be necessary to study the formation of spatiotemporal patterns even in systems with short-term memory. At the same time, our work opens up a new window into the control of these patterns using memory.

Exponential system-size dependence of the lifetime of transient spiral chaos in excitable and oscillatory media

Excitable media can develop spiral chaos, in which the number of spirals changes chaotically with time. Depending on parameter values in dynamical equations, spiral chaos may permanently persist or spontaneously arrive at a steady state after a transient time, referred to as the lifetime. Previous numerical studies have demonstrated that the lifetime of transient spiral chaos increases exponentially with system size to a good approximation. In this study, using the fact that the number of spirals obeys a Gaussian distribution, we provide a general expression for the system size dependence of the lifetime for large system sizes, which is indeed exponential. We confirm that the expression is in good agreement with numerically obtained lifetimes for both excitable and oscillatory media with parameter sets near the onset of transient chaos. The expression we develop for the lifetime is expected to be useful for predicting lifetimes in large systems.

Self-organized alternating chimera states in oscillatory media

Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and desynchronized regions, respectively, are of the same size, the symmetry of the system predicts that interchanging both phases still gives a solution to the underlying equations. We observe this kind of interchange as a self-emerging phenomenon in an oscillatory medium with nonlinear global coupling. An interplay between local and global couplings renders the formation of these alternating chimeras possible.

Theoretical analysis of defect-mediated turbulence in a catalytic surface reaction

We present a statistical analysis of defect-mediated turbulence in a kinetic model of catalytic CO oxidation on Pt(110). A probabilistic description based on the gain and loss rates of defects is derived. For low values of the CO partial pressure the statistics of topological defects agree with earlier results for the complex Ginzburg-Landau equation. For high values of the CO partial pressure, we observe an additional autocatalytic reproduction of defects that results in a linear dependence of the defect creation rate on the number of defects in the system. The role of correlations between defects of opposite topological charge was found to be weaker than in the experimental system.

Period doubling and spatiotemporal chaos in periodically forced CO oxidation on Pt(110)

Periodic forcing of chemical turbulence in the catalytic CO oxidation on Pt(110) can induce a period doubling cascade to chaos. Using a forcing frequency near the second harmonic of the system's natural frequency, and carefully increasing the forcing amplitude, the system successively exhibits spiral wave turbulence, resonant pattern formation, and chaotic oscillations. In the latter case, global coupling induces strong spatial correlation. Experimental results are presented as well as numerical simulations using a realistic model. Good agreement is found between experiment and theory. The results give further insight into the complex nature of reaction-diffusion systems and are of high importance regarding control strategies on such systems. The presented setup enhances the range of achievable dynamical states and allows for new experimental investigations on the dynamics of extended oscillatory systems.

Defect-mediated turbulence in the Belousov-Zhabotinsky reaction

Statistical properties of topological defects in defect-mediated turbulence due to the Doppler instability are examined experimentally in the Belousov-Zhabotinsky reaction. By applying the phase space reconstruction approach, processes of defect creation, annihilation, and defect movement are analyzed. The defect dynamics can be well interpreted within the framework of stochastic Markovian process. In contrast to previous studies that made direct measure of the gain and loss rates, which is practically difficult, we demonstrate that the rates can be obtained directly from the analysis of the time series of defects, and the shape of the probability distribution function can be reproduced in a simple way.

Pattern formation in 4:1 resonance of the periodically forced CO oxidation on Pt(110)

Periodically forced oscillatory reaction-diffusion systems may show complex spatiotemporal patterns. At high-frequency resonant forcing, multiple-phase patterns can be found. In the present work, the dynamics of turbulent CO oxidation on Pt(110), forced with the fourth harmonic of the system's natural frequency, is investigated. Experiments result in subharmonic entrainment, where the system locks to a quarter of the forcing frequency. Cluster patterns are observed, where different parts of the pattern show a defined phase difference. The experimental results are compared with numerical simulations using the realistic Krischer-Eiswirth-Ertl model for catalytic CO oxidation. Using the fourth harmonic of an uncoupled surface element's natural frequency, we find 3:1 entrainment with three-phase cluster patterns in a wide parameter range of forcing amplitudes and frequency detuning. Numerical analysis of the spatially extended, turbulent system reveals a remarkable upshift of the mean oscillation frequency compared to homogeneous oscillations. Using the fourth harmonic of the most prominent frequency found in the turbulent system results in four-phase patterns with partial or full 4:1 entrainment, depending on the forcing parameters chosen.