2017/05/19 by Debdipta Goswami, Subhankar Ray, Goswami, Debdipta +1
Computer Science · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaos control and synchronization #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1705.07101
5 pages, 15 figures
arxiv created 2017/05/19 · openalex publication_date 2017/05/19 · arxiv updated 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simple electronic circuit with a voltage controlled current source is investigated. The circuit exhibits rich dynamics upon varying the circuit elements such as L,C and R, and the control factor of the current source. Among several other interesting features, the circuit demonstrates two local bifurcations, namely, node to spiral and Hopf bifurcation, and a global homoclinic bifurcation. Phase-portraits corresponding to these bifurcations are presented and the implications of these bifurcations on system stability are discussed. In particular, the circuit parameters corresponding to the onset of Hopf bifurcation may be exploited to design an oscillator with stable frequency and amplitude. The circuit may be easily implemented with nonlinear resistive elements such as diodes or transistors in saturation and a gyrator block as the voltage controlled current source.