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| We consider systems where a vector field is diffusively coupled to the zero field.
In a particle interpretation such systems describe particles switching between
an active and a quiescent phase. We apply this concept to delay equations and
derive three distinct classes of vector valued delay equations with quiescent
phases showing different qualitative behavior.
Quiescent phases leave stationary points unchanged but affect stability, oscillatory
behavior, Hopf bifurcations, and periodic orbits. When all components of the solution
vector go quiescent with the same rates, then quiescent phases act like damping.
If different components go quiescent with different rates then there may be excitation
phenomena: stable stationary points undergo Hopf bifurcations.
In the case of two dependent variables exact conditions for these phenomena can be found. |
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