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Oscillator death in systems of coupled neural oscillators. (English) Zbl 0686.34033

Summary: Phase-locking in a system of oscillators that are weakly coupled can be predicted by examining a related system in which the coupling is averaged over the oscillator cycle. This fails if the coupling is large. It is shown that in the presence of large interactions, a pair or a chain of oscillators may develop a new stable equilibrium state that corresponds to the cessation of oscillation. This phenomenon is robust for neural type interactions and does not happen in systems that are weakly coupled.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
92C50 Medical applications (general)
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