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}
}
  • Jeremias Epperlein, Anne-Ly Do, +1 author Stefan Siegmund
  • Published 2013
  • Mathematics
  • Physica D: Nonlinear Phenomena
  • 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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