Impossibility of asymptotic synchronization for pulse-coupled oscillators with delayed excitatory coupling.
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz 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.
Wu
Wei
W
Fudan University, Shanghai Key Laboratory for Contemporary Applied Mathematics, Shanghai, 200433, PR China. wuweifd@vip.sina.com
Chen
Tianping
T
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001522:Behavior, Animal / Q000502:physiology; D001683:Biological Clocks / Q000502:physiology*; D002490:Central Nervous System / Q000502:physiology*; D003198:Computer Simulation; D003344:Cortical Synchronization; D019706:Excitatory Postsynaptic Potentials / Q000502:physiology; D048888:Fireflies / Q000502:physiology*; D049449:Luminescence; D055641:Mathematical Concepts; D023421:Models, Animal; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D011930:Reaction Time / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology*