Abstract
The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.
Highlights
The behavior of large ensembles of out of equilibrium units is far from being completely understood
Some bridges have been built to connect the dynamics of individual units with the collective state of a network
This line of work has a long and rich history that includes the pioneering work of Art Winfree, who presented the first mathematical models built to describe the synchronization between biological oscillators [5,6]
Summary
The behavior of large ensembles of out of equilibrium units is far from being completely understood. Yoshiki Kuramoto made important advances in this line of work He proposed a simple model for the behavior of a large set of coupled oscillators, interacting pairwise through a sinusoidal function of their phase differences [7,8]. In this approach, the collective behavior of the system is described in terms of a single complex number: its amplitude accounts for the phase-coherence of the population of oscillators, and its phase stands for the average phase. In the second part of this work (Sections 3 and 4), we discuss how the macroscopic variable defined in Section 2 compares to the local field potential (LFP), and we test this relationship using measurements in an actual nervous system
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