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Time-delayed feedback in neurosystems. (English) Zbl 1185.34108

Summary: The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.

MSC:

34K20 Stability theory of functional-differential equations
92C20 Neural biology
93C23 Control/observation systems governed by functional-differential equations
93D15 Stabilization of systems by feedback
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