Collective chaos in pulse-coupled neural networks

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the onset of various chimera states as well as to a new regime, where the two populations are characterized by a different degree of synchronization. Symmetric collective states of increasing dynamical complexity are also observed. The computation of the the finite-amplitude Lyapunov exponent allows us to establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.Comment: 6 pages, 5 eps figures, to appear on Europhysics Letters in 201

Chaos in generically coupled phase oscillator networks with nonpairwise interactions

The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling - including three and four-way interactions of the oscillator phases - that appears generically at the next order in normal-form based calculations, can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values

Chimera states in pulse coupled neural networks: the influence of dilution and noise

We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one population is fully synchronized and the other is in a state of partial synchronization (PS) as well as generalized chimera states, where both populations are in PS, but with different levels of synchronization. Symmetric macroscopic states are also present, ranging from quasi-periodic motions, to collective chaos, from splay states to population anti-phase partial synchronization. We then investigate the influence disorder, random link removal or noise, on the dynamics of collective solutions in this model. As a result, we observe that broken symmetry chimera-like states, with both populations partially synchronized, persist up to 80 \% of broken links and up to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the introduction of disorder on symmetric chaotic state has a constructive effect, namely to induce the emergence of chimera-like states at intermediate dilution or noise level.Comment: 15 pages, 7 figure, contribution for the Workshop "Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT" held in Turin (Italy) in September 201

Synchronization of clocks

Peer reviewedPostprin

Realizing the physics of motile cilia synchronization with driven colloids

Cilia and flagella in biological systems often show large scale cooperative behaviors such as the synchronization of their beats in "metachronal waves". These are beautiful examples of emergent dynamics in biology, and are essential for life, allowing diverse processes from the motility of eukaryotic microorganisms, to nutrient transport and clearance of pathogens from mammalian airways. How these collective states arise is not fully understood, but it is clear that individual cilia interact mechanically,and that a strong and long ranged component of the coupling is mediated by the viscous fluid. We review here the work by ourselves and others aimed at understanding the behavior of hydrodynamically coupled systems, and particularly a set of results that have been obtained both experimentally and theoretically by studying actively driven colloidal systems. In these controlled scenarios, it is possible to selectively test aspects of the living motile cilia, such as the geometrical arrangement, the effects of the driving profile and the distance to no-slip boundaries. We outline and give examples of how it is possible to link model systems to observations on living systems, which can be made on microorganisms, on cell cultures or on tissue sections. This area of research has clear clinical application in the long term, as severe pathologies are associated with compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic

Time-delayed feedback in neurosystems

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure