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. 2018 May 3;8:6949. doi: 10.1038/s41598-018-24670-y

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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In the relaxation oscillator (equations (11,12,13)) the coupling field S reflects the oscillation wave form and affects the stability of the fixed point. (A) Temporal evolution of x, y, and S for the relaxation oscillator and (B) corresponding projection onto the (x, y)-phase plane. Black: x-nullcline, gold: y-nullclines corresponding to the minimal (solid) and the maximal (dashed) value of S along the limit cycle. Parameters: $ϵ = 0.05$ , β = 3, μ = 0.2, λ = 0.05, ν = 2, κ_local = 5, κ_global = 0.15, $x_{0}^{(1)} = - 2$ , $x_{0}^{(2)} = - 1.2$ , γ = 2.5, σ = 0.