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Ubiquity of ring structures in the control space of complex oscillators

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Ramirez Avila,  Gonzalo M.
Potsdam Institute for Climate Impact Research;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

Gallas,  Jason A. C.
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Citation

Ramirez Avila, G. M., Kurths, J., Gallas, J. A. C. (2021): Ubiquity of ring structures in the control space of complex oscillators. - Chaos, 31, 10, 101102.
https://doi.org/10.1063/5.0066877


Cite as: https://publications.pik-potsdam.de/pubman/item/item_27054
Abstract
We report the discovery of two types of stability rings in the control parameter space of a vertical-cavity surface-emitting semiconductor laser. Stability rings are closed parameter paths in the laser control space. Inside such rings, laser stability thrives even in the presence of small parameter fluctuations. Stability rings were also found in rather distinct contexts, namely, in the way that cancerous, normal, and effector cells interact under ionizing radiation and in oscillations of an electronic circuit with a junction-gate field-effect transistor (JFET) diode. We argue that stability-enhancing rings are generic structures present in the control parameter space of many complex systems. Recently, high-performance computer clusters combined with reliable numerical methods have been revealing a plethora of intricate structures in stability diagrams of several complex nonlinear oscillators. This paper reports two types of stability rings observed in three rather unalike dynamical systems, namely, in the control parameter space of a state-of-the-art model of a vertical-cavity surface-emitting semiconductor laser, in a model of the dynamics of cancerous cells subjected to ionizing radiation, and in the inductor-based Hartley electronic circuit with a JFET and the usual tapped coil. Here, selected control parameter planes of these three complex oscillators are shown to display rings, i.e., closed parameter paths, formed by periodic oscillations along which the number of spikes per period remains constant or not. The existence of such stability rings cannot be predicted theoretically due to the total absence of an adequate framework to solve analytically coupled nonlinear differential equations. However, stability rings should not be difficult to validate experimentally. We believe stability rings to be generic structures present in the control parameter space of many other complex systems underlying important applications.