Chaotic attractors

Networks of interconnected neurons display diverse patterns of activity. Relating these patterns to the structure of the network is a central goal of theoretical neuroscience. Classic neural field and rate models have been powerful tools for this purpose due to their analytical tractability. Here, we show that the recently-developed combinatorial threshold-linear network (CTLN) model is a mean-field theory for excitatory-inhibitory Hawkes networks, with clustered connectivity, in an inhibition-stabilized regime. This mapping allows us to leverage powerful analytical results for CTLN networks

Networks of interconnected neurons display diverse patterns of collective spiking activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the re-activation of previously evoked patterns. Previous studies of clustered networks have focused on metastabilty between fixed points corresponding to individual clusters, leaving open the question of whether clustered spiking networks can display more rich dyna

Coherent oscillations of neural activity are ubiquitous across brain spatial and temporal scales and have been associated with the formation of sensory or behavioral representations [1]. Refined experimental techniques report today a new complexity of this oscillatory activity, especially in the gamma (30-100 Hz) band. Indeed, the frequency of these oscillations shows a large variability through time [2], questioning the classical view of γ oscillations being separated into different frequency bands. Oscillations appear instead in bursts characterised by rapid, synchronous neuronal firing. Thi

The specific topology of biological neural networks is believed to be one of the most important ingredients of the nervous system's computational capabilities. Furthermore, multiple experimental studies have demonstrated that neural connectivity is highly inhomogeneous, following different patterns between different regions and neuron types. In particular, the presence of clusters of highly interconnected neurons is one of the most well-established connectivity patterns across multiple brain areas. Still, the functional implications of such brain connectivity features, especially for the perfo