Various oscillation patterns in phase models with locally attractive and globally repulsive couplings.

@article{Sato2015VariousOP,
  title={Various oscillation patterns in phase models with locally attractive and globally repulsive couplings.},
  author={Katsuhiko Sato and Shin-ichiro Shima},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={92 4},
  pages={
          042922
        }
}
  • Katsuhiko Sato, S. Shima
  • Published 28 October 2015
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three… 

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References

SHOWING 1-10 OF 37 REFERENCES
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Equilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index
Chemical oscillations
A chemical reaction is usually thought of as coming together of reactant molecules to form products. The concentrations of initial components (reactants) decrease, and concentrations of products
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
TLDR
The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods.
Nature
  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
Phys
  • Rev. E 48, 3470
  • 1993
Prog. Biophys. Mol. Biol
  • Prog. Biophys. Mol. Biol
  • 2011
Prog. Biophys. Mol. Biol
  • Prog. Biophys. Mol. Biol
  • 2011
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 2013
Chemical Oscillations, Waves, and Turbulence
...
...