Noise-sustained coherent oscillation of excitable media in a chaotic flow

The role of noise in a predator-prey model with Allee effect

The existence and implications of alternative stable states in ecological systems have been investigated extensively within deterministic models. However, it is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. Thus, in this paper, we study the role of noise on the pattern formation of a spatial predator-prey model with Allee effect. The obtained results show that the spatially extended system exhibits rich dynamic behavior. More specifically, the stationary pattern can be induced to be a stable target wave when the noise intensity is small. As the noise intensity is increased, patchy invasion emerges. These results indicate that the dynamic behavior of predator-prey models may be partly due to stochastic factors instead of deterministic factors, which may also help us to understand the effects arising from the undeniable susceptibility to random fluctuations of real ecosystems.

Noise can delay and advance the collapse of spatiotemporal chaos

Spatiotemporal chaos on a regular ring network of excitable Gray-Scott dynamical elements collapses to a stable asymptotic state. We find that the addition of dynamical noise clearly influences the spatiotemporal pattern and the transient lifetime of spatiotemporal chaos. Spatially uniform noise significantly decreases the average lifetime of spatiotemporal chaos due to an enlargement of regions of local collapse. For spatially inhomogeneous noise the collapse is maximally delayed at an intermediate noise level, but drastically advanced for larger noise levels.

Mixing efficiency in an excitable medium with chaotic shear flow

The effect of a time-periodic chaotic shear flow on an excitable chemical medium is studied numerically. Stirring effects on pattern formation strongly depend on the shear amplitude and the ratio of the advective and chemical time scales (Damköhler number, Da). We have observed that the wave period increases with decreasing Da below some critical value, afterwards the period decreases until complete wave annihilation. In the last case, before final extinction, a set of uncorrelated, nonstationary excitable dots survive, whose number depends on the mixing rate. Insights on the nature of this critical behavior are obtained through the calculation of the mixing efficiency of the flow.

Active media under rotational forcing

The bubble-free Belousov-Zhabotinsky reaction has been used to study the effects of centrifugal forces on autowave propagation. The reaction parameters were chosen such that the system oscillates naturally creating target waves. In the present study, the system was forced to rotate with a constant velocity around a central axis. In studying the effects of such a forcing on the system, we focused on target dynamics. The system reacts to this forcing in different ways, the most spectacular being a dramatic increase in the period of the target, the effect growing stronger as we move away from the center of rotation. A numerical study was carried out using the two-variable Oregonator model, modified to include convective effects through the diffusion coefficient. The numerical results showed a good qualitative agreement with those of the experiments.

Resonant pattern formation in active media driven by time-dependent flows

The effect of a time-dependent flow in an oscillatory chemical system supporting front propagation is studied. Resonant target patterns depend on the strength and frequency of the time-dependent flow. The flow time scale needed to entrain the system to the resonant target period of oscillation depends on the closeness to the natural oscillation frequency of the medium. The flow strength needed to obtain these patterns is interpreted in terms of mixing optimization, and we give conditions for the flow that guarantee the best mixing with the Bernoulli property.

Bifurcations in reaction-diffusion systems in chaotic flows

We study the behavior of reacting tracers in a chaotic flow. In particular, we look at an autocatalytic reaction and at a bistable system which are subjected to stirring by a chaotic flow. The impact of the chaotic advection is described by a one-dimensional phenomenological model. We use a nonperturbative technique to describe the behavior near a saddle node bifurcation. We also find an approximation of the solution far away from the bifurcation point. The results are confirmed by numerical simulations and show good agreement.

Experimental studies of pattern formation in a reaction-advection-diffusion system

Experiments are presented on pattern formation in the Belousov-Zhabotinsky (BZ) reaction in a blinking vortex flow. Mixing in this flow is chaotic, with nearby tracers separating exponentially with time. The patterns that form in this flow with the BZ reaction mimic chaotic mixing structures seen in passive transport. The behavior is analyzed in terms of a mixing time taum and a characteristic decorrelation time TBZ for the BZ system. Flows with taum comparable to or smaller than TBZ generate large-scale patterns whose features are captured by simulations of mixing fields for the flow.