Effect of local feedback on Turing pattern formation

Target Turing patterns and growth dynamics in the chlorine dioxide-iodine-malonic acid reaction

We study the growth dynamics of Turing patterns in the chlorine dioxide-iodine-malonic acid reaction-diffusion system in response to perturbations with visible light. We describe several mechanisms by which Turing patterns reappear after they are suppressed by illumination with a disc-shaped geometry. We observe that under specific conditions the patterns reorganize from a random configuration of spots and stripes to a set of ordered, concentric rings, which we refer to as target Turing patterns. These patterns closely resemble the unit cells of the Turing hexagonal superlattices known as black eye patterns. However, these target Turing patterns are not part of a larger superlattice structure, and they usually have a larger number of concentric rings. Numerical simulations support the experimental findings.

Control of the Hopf-Turing transition by time-delayed global feedback in a reaction-diffusion system

Application of time-delayed feedback is a practical method of controlling bifurcations in reaction-diffusion systems. It has been shown that for a suitable feedback strength, time delay beyond a threshold may induce spatiotemporal instabilities. For an appropriate parameter space with differential diffusivities of the activator-inhibitor species, delayed feedback may generate Turing instability via a Hopf-Turing transition, resulting in stationary patterns. This is explored by a theoretical scheme in a photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system where the delayed feedback is externally tuned by photoillumination intensity. Our analytical results corroborate with direct numerical simulations.

Time-delay-induced instabilities in reaction-diffusion systems

Time delay in the kinetic terms of reaction-diffusion systems has been investigated. It has been shown that short delay beyond a critical threshold may induce spatiotemporal instabilities. For unequal diffusivities and appropriate parameter space delay may induce Turing instability resulting in stationary patterns and also interesting Turing-Hopf transition with the formation of spirals. The theoretical scheme has been numerically explored in two different prototypical reaction-diffusion systems.