Delay-induced inward and outward spiral waves in oscillatory medium

Selection of spatiotemporal patterns in arrays of spatially distributed oscillators indirectly coupled via a diffusive environment

Emergence of self-organized behaviors in diverse living systems often depends on population density. In these systems, cell-cell communications are usually mediated by the surrounding environment. Collective behaviors (e.g., synchrony and dynamical quorum sensing) of such systems with stirred environment have been extensively studied, but the spatiotemporal dynamics of the oscillators coupled via a diffusive environment (without stirring) is rather understudied. We here perform a computational study on the selection and competition of wave patterns in arrays of spatially distributed oscillators immersed in a diffusive medium. We find that population density plays a crucial role in the selection of wave patterns: (i) for a single spiral in the system, its rotation either inward or outward could be controlled by population density, and (ii) for spiral and target waves coexisting initially in the system, wave competition happens and population density decides which type of wave will finally survive. The latter phenomenon is further confirmed in a system whose individual element is excitable rather than self-sustained oscillatory. The mechanism underlying all these observations is attributed to the frequency competition. Our results in the excitable case may have implications on the experimental results.

Entoptic perceptions of spiral waves and rare inward spirals

This report concerns Entoptic Rotating Spiral Waves as observed and documented by the author over a period of 46 years (1962-2008). The manifestations of these state-dependent, elusive rotating spiral entities were brief, emerging only during sleep-to-waking arousal epochs (in limbo). The images were seen only with closed lids in favorable ambient lighting-here, termed the umbral view. The clusters of rotating spiral entities emerge briefly to conscious view; their angular subtenses are estimated to be between 1° and 4°, and the rotations at ten-turns per second. Epochs of these activities commonly continued for about 20 s, with longevity of each visible entity up to 4 s. 90% of all observed entities were circular and outwardly levorotary; 5% were elliptical, appearing only as horizontal (prolate) entities. Overlapping units were rare, and were chiefly elliptical. Observations of twin spirals were also rare, seen in counter rotations, each twin inwardly rotating.

Chiralities of spiral waves and their transitions

The chiralities of spiral waves usually refer to their rotation directions (the turning orientations of the spiral temporal movements as time elapses) and their curl directions (the winding orientations of the spiral spatial geometrical structures themselves). Traditionally, they are the same as each other. Namely, they are both clockwise or both counterclockwise. Moreover, the chiralities are determined by the topological charges of spiral waves, and thus they are conserved quantities. After the inwardly propagating spirals were experimentally observed, the relationship between the chiralities and the one between the chiralities and the topological charges are no longer preserved. The chiralities thus become more complex than ever before. As a result, there is now a desire to further study them. In this paper, the chiralities and their transition properties for all kinds of spiral waves are systemically studied in the framework of the complex Ginzburg-Landau equation, and the general relationships both between the chiralities and between the chiralities and the topological charges are obtained. The investigation of some other models, such as the FitzHugh-Nagumo model, the nonuniform Oregonator model, the modified standard model, etc., is also discussed for comparison.

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.