Controlling the Chimera Form in the Leaky Integrate-and-Fire Model.

We study the influence of broken connectivity and frequency disorder in systems of coupled neuronal oscillators. Under nonlocal coupling, systems of nonlinear oscillators, such as Kuramoto, FitzHugh-Nagumo, or integrate-and-fire oscillators, demonstrate nontrivial synchronization patterns. One of these patterns is the "chimera state," which consists of coexisting coherent and incoherent domains. In networks of biological neurons, the connectivity is not always perfect, but might be locally broken or interrupted due to pathologies, neuron degenerative disorders, or accidents. Our simulations show that destructed connectivity drastically affects synchronization, driving the coherent parts of the chimera state to cover symmetrically the region where the anomaly is located. The network synchronization decreases with the size of the destructed region as evidenced by the Kuramoto synchronization index. To the contrary, when keeping the connectivity of all nodes intact, altering the frequency in a block of oscillators drives the incoherent part of the chimera state toward the anomaly. This work is in line with recent dynamical approaches aiming to locate anomalies in the structure of brain networks, in particular when the anomalies have small, difficult-to-detect sizes.

Successful network inference from time-series data using mutual information rate.

This work uses an information-based methodology to infer the connectivity of complex systems from observed time-series data. We first derive analytically an expression for the Mutual Information Rate (MIR), namely, the amount of information exchanged per unit of time, that can be used to estimate the MIR between two finite-length low-resolution noisy time-series, and then apply it after a proper normalization for the identification of the connectivity structure of small networks of interacting dynamical systems. In particular, we show that our methodology successfully infers the connectivity for heterogeneous networks, different time-series lengths or coupling strengths, and even in the presence of additive noise. Finally, we show that our methodology based on MIR successfully infers the connectivity of networks composed of nodes with different time-scale dynamics, where inference based on Mutual Information fails.

Complex statistics and diffusion in nonlinear disordered particle chains.

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10(9), our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.