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The coupling matrix for the network can be asymmetric.
In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear.
Additionally, we investigated the choice of inner coupling matrix to get a desirable self-synchronization speed.
In particular, the generalized coupling matrix of this network can be asymmetric and weighted.
We use Lyapunov functions to establish general theoretical conditions for designing the coupling matrix.
What is more, the coupling matrix is not assumed to be symmetric or irreducible.
It is usual in network models that scale and topology are represented by outer coupling matrix.
First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix.
We design band pass filter using general coupling matrix synthesis methods with Chebyshev filtering function.
For these networks, the eigenvalues of the outer coupling matrix are all non-positive.
In order to avoid numerical instability, the joint coupling matrix is utilized.
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