Effects of symmetry-breaking on the dynamics of the Shinriki’s oscillator

• Published in: The European physical journal. ST, Special topics Special topics, 2021-08, Vol.230 (7-8), p.1813-1827
• Main Authors: Kengne, Léandre Kamdjeu, Kengne, Romanic, Njitacke, Zeric Tabekoueng, Fonzin, Theophile Fozin, Pone, Roger Mboupda, Tagne, Hervé Thierry Kamdem
• Format: Article
• Language: English
• Subjects: Asymmetry; Atomic; Bifurcations; Broken symmetry; Circuit Application of Chaotic Systems: Modeling; Circuits; Classical and Continuum Physics; Condensed Matter Physics; Dynamical Analysis and Control; Liapunov exponents; Materials Science; Mathematical models; Measurement Science and Instrumentation; Molecular; Nonlinear analysis; Optical and Plasma Physics; Parameters; Physics; Physics and Astronomy; Regular Article; Semiconductor diodes; Symmetry
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-021-00130-z

We investigate the dynamics of the well-known Shinriki’s oscillator both in its symmetric and asymmetric modes of operation. Instead of using the classical approximate cubic model of the Shinriki’s oscillator, we propose a close form model by exploiting the Shockley exponential diode equation. The proposed model takes into account the intrinsic characteristics of semiconductor diodes forming the nonlinear part (i.e., the positive conductance). We address the realistic issue of symmetry-breaking by considering different numbers of diodes within the two branches of the positive conductance. The dynamics of the system is investigated by exploiting conventional nonlinear analysis tools such as bifurcation diagrams, phase-space trajectories plots, basins of attractions, and graphs of Lyapunov exponent as well. In the symmetric mode of operation, the system experiences coexisting symmetric attractors, period-doubling route to chaos, and merging crisis. The symmetry breaking analysis yields two asymmetric coexisting bifurcation branches (i.e., asymmetric bi-stability) each of which exhibits its own sequence of bifurcations to chaos when monitoring the main control parameter. In this special mode, the merging process never occurs; instead, one of the bifurcation branches vanishes when decreasing the control parameter beyond a critical value following a crisis event. The theoretical results are validated by carrying out laboratory experimental studies of the physical circuit.