Decomposing the Dynamics of Delayed Networks: Equilibria and Rhythmic Patterns in Neural Systems
Time Delay Systems, Volume # 10 | Part# 1
Digital Object Identifier (DOI)
Biology; Stability and stabilisation
A method is presented that allows one to decompose the dynamics of networked dynamical systems with time-delayed coupling. The key idea is to ``block-diagonalize" the system with the help of the eigenvectors of the coupling matrix. While large delayed networks are difficult to handle both analytically and numerically, the ``small" blocks obtained by the decomposition can be investigated using standard methods. The proposed technique is applied to a neural network where the stability of the synchronized equilibria and periodic solutions are investigated. The methodology may also be applied for large engineered networks like electric power grids.
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