Pulse Coupled Oscillator Networks

Chapter
Part of the Analog Circuits and Signal Processing book series (ACSP, volume 124)

Abstract

In a seminal 1990 work (SIAM J Appl Math 50:1645–1662, 1990), Mirollo and Strogatz posed a general analytical framework for pulse coupled oscillator systems as a behavioral model for Southeast Asian Fireflies that has subsequently been extensively studied in the fields of mathematics, physics, and non-linear dynamics. The system assumes a network ofN oscillators which interact through impulsive coupling, representing the “firing” of a firefly. Each oscillator with indexj has an internal state that can be represented by a phase variableϕ j (t), which increases in time at a constant rate\({{\phi }_{j}}\text{ }\!\!~\!\!\text{ }=\text{ }\!\!~\!\!\text{ }1+{{\delta }_{j}}\), where the parameter\(\left| {{\delta }_{j}} \right|\) models variability in the natural oscillation period of oscillatorj in the absence of coupling.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Cornell UniversityIthacaUSA

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