  We investigate the dynamical behaviour 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.
