Resonance-induced oscillons in a reaction-diffusion system

Robust controlled formation of Turing patterns in three-component systems

Over the past few decades, formation of Turing patterns in reaction-diffusion systems has been shown to be the underlying process in several examples of biological morphogenesis, confirming Alan Turing's hypothesis, put forward in 1952. However, theoretical studies suggest that Turing patterns formation via classical "short-range activation and long-range inhibition" concept in general can happen within only narrow parameter ranges. This feature seemingly contradicts the accuracy and reproducibility of biological morphogenesis given the stochasticity of biochemical processes and the influence of environmental perturbations. Moreover, it represents a major hurdle to synthetic engineering of Turing patterns. In this work it is shown that this problem can be overcome in some systems under certain sets of interactions between their elements, one of which is immobile and therefore corresponding to a cell-autonomous factor. In such systems Turing patterns formation can be guaranteed by a simple universal control under any values of kinetic parameters and diffusion coefficients of mobile elements. This concept is illustrated by analysis and simulations of a specific three-component system, characterized in absence of diffusion by a presence of codimension two pitchfork-Hopf bifurcation.

Parametric spatiotemporal oscillation in reaction-diffusion systems

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

Formation of spiral waves with substructure in a bursting media

Formation of spiral waves in a bursting media is investigated. Due to the multiple timescale oscillation of the local dynamics, an interesting substructure of traveling wave (STW) is observed in the spiral arm. As a result of the special moving media formed by neurons in the spiral arm, STWs propagate from the spiral tip to far field with an increasing wave length and move faster along the front of the spiral arm than along the back, leading to the formation of fragments in STWs. Moreover, we find that a sharp change of stimulus current can lead to backfiring of STWs, which may break the spiral wave front and further result in the formation of a multi-spiral pattern.

Synthetic homeostatic materials with chemo-mechano-chemical self-regulation

Living organisms have unique homeostatic abilities, maintaining tight control of their local environment through interconversions of chemical and mechanical energy and self-regulating feedback loops organized hierarchically across many length scales. In contrast, most synthetic materials are incapable of continuous self-monitoring and self-regulating behaviour owing to their limited single-directional chemomechanical or mechanochemical modes. Applying the concept of homeostasis to the design of autonomous materials would have substantial impacts in areas ranging from medical implants that help stabilize bodily functions to 'smart' materials that regulate energy usage. Here we present a versatile strategy for creating self-regulating, self-powered, homeostatic materials capable of precisely tailored chemo-mechano-chemical feedback loops on the nano- or microscale. We design a bilayer system with hydrogel-supported, catalyst-bearing microstructures, which are separated from a reactant-containing 'nutrient' layer. Reconfiguration of the gel in response to a stimulus induces the reversible actuation of the microstructures into and out of the nutrient layer, and serves as a highly precise 'on/off' switch for chemical reactions. We apply this design to trigger organic, inorganic and biochemical reactions that undergo reversible, repeatable cycles synchronized with the motion of the microstructures and the driving external chemical stimulus. By exploiting a continuous feedback loop between various exothermic catalytic reactions in the nutrient layer and the mechanical action of the temperature-responsive gel, we then create exemplary autonomous, self-sustained homeostatic systems that maintain a user-defined parameter--temperature--in a narrow range. The experimental results are validated using computational modelling that qualitatively captures the essential features of the self-regulating behaviour and provides additional criteria for the optimization of the homeostatic function, subsequently confirmed experimentally. This design is highly customizable owing to the broad choice of chemistries, tunable mechanics and its physical simplicity, and may lead to a variety of applications in autonomous systems with chemo-mechano-chemical transduction at their core.

Localized patterns in reaction-diffusion systems

We discuss a variety of experimental and theoretical studies of localized stationary spots, oscillons, and localized oscillatory clusters, moving and breathing spots, and localized waves in reaction-diffusion systems. We also suggest some promising directions for future research in this area.