Death island boundaries for delay-coupled oscillator chains

We present a simple analysis for obtaining the death island boundaries for delay-coupled limit cycle oscillator chains. We show analytically that for identical oscillators with nearest neighbour coupling, only two curves define the island boundary completely. An analytical ordering of eigenvalues of the stability matrix about the death island has been obtained. The difference between the island structure for even and odd number of oscillators is explained through the dependence of the boundary curves on N. A geometric picture to understand why only two modes are important in describing the boundary is also provided.