Narrow Results

We examined the dynamics of clot growth in vitro and found, that initially the clot grows at a constant speed, then abruptly stops and becomes surrounded by an "inhibition zone" in which coagulation is strongly suppressed. We also observed formation of "stratified structures" (target patterns) in which solid layers alternate with liquid blood. The experimental results strongly support a hypothesis that blood is a new type of excitable medium.

We constructed a mathematical model of clotting, which is based on a current view of the molecular pathways of blood coagulation. Several hypothetical reactions are introduced to allow accurate description of the spatio-temporal dynamics of blood clotting. The resulting model describes well all spatio-temporal aspects of clotting, as well as data obtained in the homogeneous systems.

The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular automata. Each cell gets info about states of its closest neighbors via incoming links. A link can be "conductive" or "nonconductive". States of every link are updated depending on the states of cells the link connects. Every cell of a memristive automaton assumes three states: resting, excited (analog of positive polarity) and refractory (analog of negative polarity). A cell updates its state depending on states of its closest neighbors which are connected to the cell via "conductive" links. We study behavior of memristive automata in response to point-wise and spatially extended perturbations, structure of localized excitations coupled with topological defects, interfacial mobile excitations and growth of information pathways.

We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if the number of excited neighbors lies in a certain interval (excitation interval). An excited cell becomes refractory independently on states of its neighbors. A refractory cell returns to a resting state only if the number of excited neighbors belong to recovery interval. The model is an excitable cellular automaton abstraction of a spatially extended semi-memristive medium where a cell's resting state symbolizes low-resistance and refractory state high-resistance. The medium is semi-memristive because only transition from high- to low-resistance is controlled by the density of local excitation. We present a phenomenological classification of the automata behavior for all possible excitation intervals and recovery intervals. We describe eleven classes of cellular automata with retained refractoriness based on the criteria of space-filling ratio, morphological and generative diversity, and types of traveling localizations.

A thin-layer Belousov–Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates — Fredkin gate and Toffoli gate — in a BZ medium network of excitable channels with subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates’ design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment — logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

Complex-periodic spiral waves are investigated extensively in the oscillatory medium. In this paper, the linearly polarized electric field (LPEF) is employed to induce complex-periodic spiral waves in the excitable medium with abnormal dispersion. As the amplitude of LPEF is increased beyond a threshold, the simple-periodic spiral wave converts into an irregularly complex-periodic one, in which, the local dynamics exhibit several regular spikes followed by one missed spiking period. Furthermore, with the increase of the LPEF amplitude, the missed spiking period follows different numbers of regular spikes [so-called period-1 (P-1), period-2 (P-2), etc.], even a mix of different periods. Meanwhile, the wavelength of the spiral wave transits from a short to a longer one. The pure-periodic (from P-6 to P-2) spirals generally contain defect lines, across which the phase of local oscillation changes by $2\pi$. In contrast, there is no defect line in the mixed-periodic spiral waves. This finding indicates that the defect line is not a necessary feature for complex-periodic spiral waves. Moreover, three types of tip trajectories of pure-periodic spiral waves are identified depending on the periods. That is, the outward-petal meandering, the outward-petal meandering with slow modulation, and drifting tip motion, and the tip trajectories could be used to distinguish them from the complex-oscillatory spiral waves.