Pulse-coupled decentral synchronization

Authors

R. Mathar, J. Mattfeldt,

Abstract

        Synchronous firing of biological oscillators is explained by a mathematical model developed by Mirollo and Strogatz. Exactly the same principles may be carried over to achieve decentral synchronization in TDMA-Systems. However, some extensions of the basic model are necessary in view of technical implementations. This paper deals with synchronization in finite time for two oscillators, and convergence to synchrony except on a set of initial conditions of measure zero for cliques of oscillators, particularly for nondifferentiable (e.g. piecewise linear) state functions. Moreover, for oscillator pairs we prove synchronization even if there is a certain delay between transmission and reception of pulses. A simulation tool, named ImDeSy, is developed to investigate general networks of oscillators with an arbitrary topology and more refined reaction strategies. This is demonstrated in two extensive examples.

BibTEX Reference Entry 

@article{MaMa96b,
	author = {Rudolf Mathar and J{\"u}rgen Mattfeldt},
	title = "Pulse-coupled decentral synchronization",
	pages = "1094-1106",
	journal = "SIAM Journal on Applied Mathematics",
	volume = "56",
	number = "4",
	month = Aug,
	year = 1996,
	}

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