On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

• Published in: Physica scripta 2021-12, Vol.96 (12), p.125269
• Main Authors: Ngamsa Tegnitsap, Joakim Vianney, Saatsa Tsefack, Merlin Brice, Megam Ngouonkadi, Elie Bertrand, Fotsin, Hilaire Bertrand
• Format: Article
• Language: English
• Subjects: chaos and transient chaos; coexistence of solutions; LTSPICE simulations; quintic nonlinearity; triode vacuum tube; Van der Pol oscillator
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ac3ea3

In this work, the dynamic of the triode-based Van der Pol oscillator coupled to a linear circuit is investigated (Triode-based VDPCL oscillator). Towards this end, we present a mathematical model of the triode, chosen from among the many different ones present in literature. The dynamical behavior of the system is investigated using classical tools such as two-parameter Lyapunov exponent, one-parameter bifurcation diagram associated with the graph of largest Lyapunov exponent, phase portraits, and time series. Numerical simulations reveal rather rich and complex phenomena including chaos, transient chaos, the coexistence of solutions, crisis, period-doubling followed by reverse period-doubling sequences (bubbles), and bursting oscillation. The coexistence of attractors is illustrated by the phase portraits and the cross-section of the basin of attraction. Such triode-based nonlinear oscillators can find their applications in many areas where ultra-high frequencies and high powers are demanded (radio, radar detection, satellites communication, etc) since triode can work with these performances and are often used in the aforementioned areas. In contrast to some recent work on triode-based oscillators, LTSPICE simulations, based on real physical consideration of the triode, are carried out in order to validate the theoretical results obtained in this paper as well as the mathematical model adopted for the triode.