Desynchronization and pattern formation in a noisy feed-forward oscillator network

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

Collective dynamics of phase-repulsive oscillators solves graph coloring problem

We show how to couple phase-oscillators on a graph so that collective dynamics "searches" for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring) into a functional optimization problem (finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system's evolution). Using a sample of graphs, we show that our method can serve as a viable alternative to the traditional combinatorial algorithms. Moreover, we show that, with the same computational cost, our method efficiently solves the harder problem of improper coloring of weighed graphs.

Resilience for stochastic systems interacting via a quasi-degenerate network

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network, two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process, which we trace back to the degenerate spectrum of the embedding support. The same phenomenon holds when the system is bound to explore a quasidegenerate network. In this case, the eigenvalues of the Laplacian operator, which governs species diffusion, accumulate over a limited portion of the complex plane. The larger the network, the more pronounced the amplification. Beyond a critical network size, a system deemed deterministically stable, hence resilient, can develop seemingly regular patterns in the concentration amount. Non-normality and quasidegenerate networks may, therefore, amplify the inherent stochasticity and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.

Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices

Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states—the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).