arXiv:2603.12878v1 Announce Type: new Abstract: The synchronized activity of neuronal populations can lead to pathological over-synchronization in conditions such as epilepsy and Parkinson disease. Such states can be desynchronized by brief electrical pulses. But when the underlying oscillating system is not known, as in most practical applications, to determine the specific times and intensities of pulses used for desynchronizaton is a difficult inverse problem. Here we propose a desynchronization scheme for neuronal models of bi-variate neural activity, with possible applications in the medical setting. Our main argument is the existence of a peculiar point in the phase space of the system, the centroid, that is both easy to calculate and robust under changes in the coupling constant. This important target point can be used in a control procedure because it lies in the region of minimal return times of the system.

arXiv:2603.04149v1 Announce Type: new Abstract: Structural and functional heterogeneity are hallmarks of cortical circuits, from broad degree distributions in the mouse connectome to diverse intrinsic neuronal timescales. Yet a mechanistic link between connectivity heterogeneity and functional diversity is lacking. To bridge this gap, we introduce a random recurrent network in which connectivity is generated by a configuration model with tunable degree heterogeneity and synaptic weights exhibiting varying levels of correlation. Using generating-functional methods, we derive a heterogeneous dynamical mean-field theory (hDMFT) with degree-conditioned stochastic dynamics. The theory shows that the interaction of partial symmetry in the weights and degree heterogeneity induces a non-Markovian memory term in the form of an emergent self-coupling whose strength scales with degree and produces a broad distribution of activity timescales. We obtain analytic stability criteria demonstrating that degree heterogeneity lowers the critical gain and localizes unstable modes onto hubs. The resulting rich dynamical landscape includes silent, chaotic, and multistable regimes, which we uncover via spectral, replica, and Lyapunov exponent analyses. We highlight the computational benefits of the observed timescale heterogeneity by revealing that, under an external input drive featuring a broadband spectrum, slow hub neurons act as integrators, demixing slow input components. Finally, instantiating the model with the empirically measured topology from the MICrONS cubic-millimeter mouse connectome explains the broad range of single-neuron timescales and their positive correlation with in-degree observed in resting-state recordings. Our results provide a mechanistic link between connectome topology, neural dynamics, and computation, identifying hubs in partially symmetric networks as a natural substrate for multiplexed processing across timescales.