Period-doubling route to chaos, bistability and antimononicity in a jerk circuit with quintic nonlinearity

• Published in: International journal of dynamics and control Vol. 7; no. 1; pp. 1 - 22
• Main Authors: Mboupda Pone, Justin Roger, Kamdoum Tamba, Victor, Kom, Guillaume Honore, Tiedeu, Alain Bertin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 13-03-2019; Springer Nature B.V
• Subjects: Analog circuits; Bifurcations; Bistability; Chaos theory; Circuits; Complexity; Computer simulation; Control; Control and Systems Theory; Dynamical Systems; Electronic circuits; Engineering; Nonlinear differential equations; Nonlinear equations; Nonlinearity; Poincare maps; Vibration; PSIM-based analog simulations; Antimonotonicity; Experimental studies; Jerk circuit with quintic nonlinearity; Bifurcation analysis; Bistability
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-018-0431-1

In this paper, the dynamics of an autonomous jerk circuit with quintic nonlinearity is investigated. The circuit is described by a set of three coupled-first order nonlinear differential equations recently introduced as memory oscillator by Sprott (Elegant chaos, algebraically simple chaotic flows, World Scientific, Singapore,
2010
). The dynamical behaviors of the system are examined with the help of common nonlinear methods such as bifurcation diagrams, largest Lyapunov exponent plot, Poincaré map as well as power density spectra. It is revealed that the system under scrutiny experiences some complex phenomena including period-doubling route to chaos, bistability and antimonotonicity. Finally, the analog simulations are carried out in PSIM and experimental electronic circuit is realized to validate the numerical results.