It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

Objective. While brain stimulation therapies such as deep brain stimulation for Parkinson's
disease (PD) can be effective, they have yet to reach their full potential across neurological …

In this review we survey the literature on mean-field coupled maps. We start with the early
works from the physics literature, arriving to some recent results from ergodic theory studying …

Adaptive dynamical networks are network systems in which the structure co-evolves and
interacts with the dynamical state of the nodes. We study an adaptive dynamical network in …

Networks of coupled dynamical units give rise to collective dynamics such as the
synchronization of oscillators or neurons in the brain. The ability of the network to adapt …

Generalized epileptic attacks, which exhibit widespread disruption of brain activity, are
characterized by recurrent, spontaneous, and synchronized bursts of neural activity that self …

Subthalamic deep brain stimulation (DBS) robustly generates high-frequency oscillations
known as evoked resonant neural activity (ERNA). Recently the importance of ERNA has …

Natural and technological networks exhibit dynamics that can lead to complex cooperative
behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal …

Introduction Neural interactions in the brain are affected by transmission delays which may
critically alter signal propagation across different brain regions in both normal and …

The study of adaptive dynamics, involving many degrees of freedom on two separated
timescales, one for fast changes of state variables and another for the slow adaptation of …