Ubiquity of ring structures in the control space of complex oscillators

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.

Chirality detected in Hartley’s electronic oscillator

“…Figure 2 shows stability diagrams obtained by counting the number of spikes (i.e., local maxima) of the periodic oscillations for the four independent variables of Hartley's oscillator. In these diagrams, it is possible to recognize a number of stability rings [25], namely cascades of adjacent closed parameter circuits, which are the objects of interest here.…”

Exploring chronomodulated radiotherapy strategies in a chaotic population model

“…The dynamical richness of the model motivated us to examine other aspects related to dynamical systems, such as the exploration of the parameter spaces as in [70], the basins of attraction, and the existence of amplitude and oscillation death followed by the resurrection of the oscillations.…”

Non-quantum chirality in a driven Brusselator

“…A common feature shared by both examples is the fact that non-quantum chirality was observed along certain parameter rings [13] in phase diagrams, namely along closed parameter paths in the control space of the oscillators. Along such rings, oscillation stability thrives even in the presence of small parameter fluctuations.…”