Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay

H.W. Broer, K. Efstathiou and E. Subramanian
Nonlinearity, 21(1), pp. 13-49, 2008
DOI: 10.1088/0951-7715/21/1/002

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We consider arbitrarily large networks of pulse coupled oscillators with non-zero delay where the coupling is given by the Mirollo-Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty interior) in an open parameter region for three or more oscillators. The evolution operator of the system can be discontinuous and we propose an improved model with continuous evolution operator.