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We investigate the dynamical behavior of two limit cycle oscillators that interact with each other via time delayed coupling and find that time delay can lead to amplitude death of the oscillators even if they have the same frequency. We demonstrate that this novel regime of amplitude ``death'' also exists for large collections of coupled identical oscillators and provide quantitative measures of this death region in the parameter space of coupling strength and time delay. Its implication for certain biological and physical applications is also pointed out.
Reddy et al. (Mon,) studied this question.