Reaction-diffusion dynamics in an oscillatory medium of finite size: pseudoreflection of waves

Enhanced response of regular networks to local signals in the presence of a fast impurity

We consider an array of inductively coupled Josephson junctions with a fast impurity (a junction with a smaller value of the critical current) and study the consequences of imposing a small amplitude periodic signal at some point in the array. We find that when the external signal is imposed at the impurity, the response of the array is boosted and a small amplitude signal can be detected throughout the array. When the signal is imposed elsewhere, minor effects are seen on the dynamics of the array. The same results have also been seen in the presence of a single fast-spiking neuron in a chain of diffusively coupled FitzHugh-Nagumo neurons.

Boundary-induced patterns in excitable systems: the structure of oscillatory domain

The present work extends our recently published study [Phys. Rev. E 73, 066224 (2006)] on a mechanism of pattern formation in excitable media due to inhomogeneous boundary conditions (BC). To that end, we analyze a pair of coupled excitable and oscillatory cells, a distributed FitzHugh Nagumo model, and a distributed five-variable model that describes CO catalytic oxidation. For the three systems we determine the structure of the oscillatory domains, composed of bands of complex firing solutions with period-adding bifurcations, and show the commonality of the structures. The obtained results account for the recently reported experimental observations of mixed-mode oscillations showing a period-adding bifurcation during CO oxidation on a disk-shaped catalytic cloth with imposed cold temperature BC.

Boundary-induced spatiotemporal complex patterns in excitable systems

We show that inhomogeneous boundary conditions (BCs) in a distributed reaction-diffusion excitable system are a natural source of permanent perturbations that can induce wave trains, which can be characterized as mixed-mode temporal oscillations and, when a parameter is varied, admit a period-adding bifurcation. To that end we analyze: a pair of coupled excitable and oscillatory cells, a distributed FitzHugh-Nagumo model, and a distributed five-variable model that describes catalytic oxidation. The obtained results account for the recently reported experimental observations of mixed-mode oscillations showing a period-adding bifurcation during oxidation on a disk-shaped catalytic cloth with imposed cold temperature BC.

Abnormal frequency locking and the function of the cardiac pacemaker

A heterogeneous reaction-diffusion medium consisting of two adjoining uniform regions is analyzed. The first region is a purely oscillatory one, while the second is bistable (oscillatory/excitable). We show that such a construction allows an abnormal domination of the low natural frequency of the oscillatory regime over the whole medium (abnormal frequency locking). Bifurcations leading to the appearance of the bistable regime are discussed as well as the specific dynamics of the bistable oscillations. The abnormal frequency-locking phenomenon could explain some dynamical properties of the cardiac pacemaker.

Pseudoreflection from interface between two oscillatory media: extended driver

The dynamics of a reaction-diffusion medium composed of two uniform self-oscillating regions is considered. We analyze the phenomenon of pseudoreflection of waves at the region's interface. The reflected waves show an unusual change of wavelength, amplitude, and period. In contrast to our previous results, here this behavior can be perceived as an action of a spatially extended higher-frequency "driver." Observed also are the interesting phenomena of the appearance of narrow transient zones near the interface and of diffusion-induced bifurcations. Furthermore, the pseudoreflection is shown to be a possible mechanism of spiral and "target" waves generation. The relevance of the obtained results to the dynamics of the cardiac sinus node is discussed.