Abstract
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. Mirollo and Strogatz (1990) proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.
This work is supported by National Science Foundation of China 60774074.
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Wu, W., Chen, T. (2009). Asymptotic Synchronization for Pulse-Coupled Oscillators with Delayed Excitatory Coupling Is Impossible. In: Yu, W., Sanchez, E.N. (eds) Advances in Computational Intelligence. Advances in Intelligent and Soft Computing, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03156-4_5
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DOI: https://doi.org/10.1007/978-3-642-03156-4_5
Publisher Name: Springer, Berlin, Heidelberg
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