Abstract
We consider a time varying delayed Cucker-Smale system in a harmonic potential field and analyze its long time collective behavior. Under appropriate assumptions on the initial data, we show the asymptotic collective behavior when the time varying delay is uniformly bounded by a sufficiently small constant. Our strategies are based on the Lyapunov functional approach, forward-backward estimate and the continuity argument. Finally, some numerical tests are performed to illustrate the theoretical result.
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