Synchronization in complex dynamical networks with nonsymmetric coupling
Subject of the paper are networks of coupled systems of the form \[ x_i'(t)=f(x_i(t))+\sum_{j=1}^N g_{ij}Ax_j(t),\quad i=1,\dots,N, \] where \(x_i(t)\in\mathbb{R}^n\) is the state variable of one node of the network, \(G=(g_{ij})\) is the coupling matrix. The authors extend the master stability method [\textit{L. Pecora, T. Carroll, G. Johnson, D. Mar}, and \textit{J. Heagy}, Chaos 7, 520--543 (1997; Zbl 0933.37030)] to obtain criteria for global synchronization, i.e. global stability of the invariant subspace \(\{ (x_1,\dots,x_N)|\;x_1=x_2=\cdots=x_N \}\). Using the technique of \textit{T. Nishikawa} and \textit{A. E. Motter} [Physica D 224, No. 1--2, 77--89 (2006; Zbl 1117.34048)], the authors include also the case, when the coupling matrix is nondiagonalizable.
scientific article; zbMATH DE number 5349262
scientific article