Target-wave to spiral-wave pattern transition in a discrete Belousov-Zhabotinsky reaction driven by inactive resin beads

Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue

Arrhythmias in cardiac tissue are related to irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. A localized region with a fraction of nonconducting links surrounded by homogeneous conducting tissue can become a source of reentry and ectopic beats. Extensive simulations in a discrete model of cardiac tissue show that a wave crossing a heterogeneous region of cardiac tissue can disintegrate into irregular patterns, provided the fraction of nonconducting links is close to the percolation threshold of the cell network. The dependence of the reentry probability on this fraction, the system size, and the degree of excitability can be inferred from the size distribution of nonconducting clusters near the percolation threshold.

Secure steganographic communication algorithm based on self-organizing patterns

A secure steganographic communication algorithm based on patterns evolving in a Beddington-de Angelis-type predator-prey model with self- and cross-diffusion is proposed in this paper. Small perturbations of initial states of the system around the state of equilibrium result in the evolution of self-organizing patterns. Small differences between initial perturbations result in slight differences also in the evolving patterns. It is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system. An alternative approach when the cover image represents the self-organizing pattern that has evolved from initial states perturbed using the dot-skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties.

Robustness of multilayer oscillator networks

We consider the robustness of multilayer networks composed of active and inactive oscillators from the viewpoint of interlayer coupling effects through the aging transition [H. Daido and K. Nakanishi, Phys. Rev. Lett. 93, 104101 (2004)]. We show in detail that two-layer networks increase or decrease their robustness depending on interlayer coupling schemes compared with single-layer networks. In addition, we find that an increase of mismatches of oscillator types (active or inactive) among interlayer-connected oscillators reduces the robustness of the networks with mean-field, chain, and diffusive interlayer couplings in two-layer networks. Moreover, we discuss the robustness of networks with more than two layers.