A ring of N = 2M identical neuron cells with piecewise linear and saturated bidirectional coupling nonlinearities is considered. The rotating wave under investigation exists for 'most' values of the coupling parameters alpha > 0 and vertical bar beta vertical bar <= alpha. The dominant Floquet multiplier is unstable and converges exponentially to 1 in the number of cells. The remaining 2M - 2 nontrivial Floquet multipliers converge exponentially to 0. A heteroclinic bifurcation curve and also the heteroclinic orbit connections are described by explicit formulas. The entire work was motivated by electrical circuit experiments.
Di Marco, M., Forti, M., Garay, B.M., Koller, M., Pancioni, L. (2016). Floquet multipliers of a metastable rotating wave in a Chua-Yang ring network. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 434, 798-836 [10.1016/j.jmaa.2015.08.072].
Floquet multipliers of a metastable rotating wave in a Chua-Yang ring network
Di Marco, Mauro;Forti, Mauro;Pancioni, Luca
2016-01-01
Abstract
A ring of N = 2M identical neuron cells with piecewise linear and saturated bidirectional coupling nonlinearities is considered. The rotating wave under investigation exists for 'most' values of the coupling parameters alpha > 0 and vertical bar beta vertical bar <= alpha. The dominant Floquet multiplier is unstable and converges exponentially to 1 in the number of cells. The remaining 2M - 2 nontrivial Floquet multipliers converge exponentially to 0. A heteroclinic bifurcation curve and also the heteroclinic orbit connections are described by explicit formulas. The entire work was motivated by electrical circuit experiments.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/982503