Synchronization in random balanced networks
Luis Carlos García del Molino1, Khashayar Pakdaman, Jonathan Touboul
1Institut Jacques Monod, CNRS UMR 7592, Université Paris Diderot, Paris Cité Sorbonne, F-750205, Paris, France.
Abstract:
Characterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matrix. We provide a low-dimensional approximation that shows the role of both the structure and disorder in the dynamics.
Related Concept Videos
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Sequence Networks of Rotating Machines
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
The Y-to-Y Circuit
Network Function of a Circuit
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...


