Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.Comment: 26 pages, 3 figure

Insights into collective cell behaviour from populations of coupled chemical oscillators.

Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Here, we show how experiments with coupled chemical oscillators can provide insights into collective behaviour in cellular systems. Two methods of coupling the oscillators are described: exchange of chemical species with the surrounding solution and computer-controlled illumination of a light-sensitive catalyst. The collective behaviour observed includes synchronisation, dynamical quorum sensing (a density dependent transition to population-wide oscillations), and chimera states, where oscillators spontaneously split into coherent and incoherent groups. At the core of the different types of behaviour lies an intracellular autocatalytic signal and an intercellular communication mechanism that influences the autocatalytic growth

Event-triggered communication for passivity and synchronisation of multi-weighted coupled neural networks with and without parameter uncertainties

A multi-weighted coupled neural networks (MWCNNs) model with event-triggered communication is studied here. On the one hand, the passivity of the presented network model is studied by utilising Lyapunov stability theory and some inequality techniques, and a synchronisation criterion based on the obtained output-strict passivity condition of MWCNNs with eventtriggered communication is derived. On the other hand, some robust passivity and robust synchronisation criteria based on output-strict passivity of the proposed network with uncertain parameters are presented. At last, two numerical examples are provided to testify the effectiveness of the output-strict passivity and robust synchronisation results

Modelling cell cycle synchronisation in networks of coupled radial glial cells

Radial glial cells play a crucial role in the embryonic mammalian brain. Their proliferation is thought to be controlled, in part, by ATP mediated calcium signals. It has been hypothesised that these signals act to locally synchronise cell cycles, so that clusters of cells proliferate together, shedding daughter cells in uniform sheets. In this paper we investigate this cell cycle synchronisation by taking an ordinary differential equation model that couples the dynamics of intracellular calcium and the cell cycle and extend it to populations of cells coupled via extracellular ATP signals. Through bifurcation analysis we show that although ATP mediated calcium release can lead to cell cycle synchronisation, a number of other asynchronous oscillatory solutions including torus solutions dominate the parameter space and cell cycle synchronisation is far from guaranteed. Despite this, numerical results indicate that the transient and not the asymptotic behaviour of the system is important in accounting for cell cycle synchronisation. In particular, quiescent cells can be entrained on to the cell cycle via ATP mediated calcium signals initiated by a driving cell and crucially will cycle in near synchrony with the driving cell for the duration of neurogenesis. This behaviour is highly sensitive to the timing of ATP release, with release at the G1/S phase transition of the cell cycle far more likely to lead to near synchrony than release during mid G1 phase. This result, which suggests that ATP release timing is critical to radial glia cell cycle synchronisation may help to understand normal and pathological brain development

The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention

Understanding how dynamic changes in brain activity control behavior is a major challenge of cognitive neuroscience. Here, we consider the brain as a complex dynamic system and define two measures of brain dynamics: the synchrony of brain activity, measured by the spatial coherence of the BOLD signal across regions of the brain; and metastability, which we define as the extent to which synchrony varies over time. We investigate the relationship among brain network activity, metastability, and cognitive state in humans, testing the hypothesis that global metastability is “tuned” by network interactions. We study the following two conditions: (1) an attentionally demanding choice reaction time task (CRT); and (2) an unconstrained “rest” state. Functional MRI demonstrated increased synchrony, and decreased metastability was associated with increased activity within the frontoparietal control/dorsal attention network (FPCN/DAN) activity and decreased default mode network (DMN) activity during the CRT compared with rest. Using a computational model of neural dynamics that is constrained by white matter structure to test whether simulated changes in FPCN/DAN and DMN activity produce similar effects, we demonstate that activation of the FPCN/DAN increases global synchrony and decreases metastability. DMN activation had the opposite effects. These results suggest that the balance of activity in the FPCN/DAN and DMN might control global metastability, providing a mechanistic explanation of how attentional state is shifted between an unfocused/exploratory mode characterized by high metastability, and a focused/constrained mode characterized by low metastability

Chaotic, informational and synchronous behaviour of multiplex networks

Acknowledgements MSB acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. This work was also partially supported by CNPq, CAPES, and Fundac¸ao Arauc ˜ aria.Peer reviewedPublisher PD

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience