# Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian

@article{Epperlein2013MesoscaleOT, title={Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian}, author={Jeremias Epperlein and Anne-Ly Do and Thilo Gross and Stefan Siegmund}, journal={Physica D: Nonlinear Phenomena}, year={2013}, volume={261}, pages={1-7} }

Abstract A linear system x = A x , A ∈ R n × n , x ∈ R n , with rk A = n − 1 , has a one-dimensional center manifold E c = { v ∈ R n : A v = 0 } . If a differential equation x = f ( x ) has a one-dimensional center manifold W c at an equilibrium x ∗ then E c is tangential to W c with A = D f ( x ∗ ) and for stability of W c it is necessary that A has no spectrum in C + , i.e. if A is symmetric, it has to be negative semi-definite. We establish a graph theoretical approach to characterize semi… CONTINUE READING

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