Dynamical study of VDPCL oscillator: antimonotonicity, bursting oscillations, coexisting attractors and hardware experiments
Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, University of Dschang, P. O. Box 67, Dschang, Cameroon
2 Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P. O. Box 134, Bandjoun, Cameroon
3 Department of Electrical and Electronics Engineering, College of Technology, University of Buea, P. O. Box 63, Buea, Cameroon
Accepted: 29 June 2020
Published online: 22 July 2020
Some years ago, Fotsin and Woafo (Phys Scrip 71:241, 2005) introduced and investigated an electronic circuit consisting of Van der Pol oscillator coupled to a linear oscillator, which appeared to be chaotic. Later, some few authors investigated chaos synchronization of this model. However, detail dynamical analyses and experimental verification of this interesting model were not carried out till now. This work thus provides a deeper dynamical analysis and experimental confirmation of the chaotic behavior in this oscillator. Some basic dynamic properties of the system are studied, namely symmetry, dissipation, fixed points with their stability and Hopf bifurcation. It is found that the system displays complicated behaviors such as intermittency, crisis route to chaos, antimonotonicity, bursting oscillations and coexisting attractors for specific values of parameters setting. The coexistence of attractors is illustrated using the phase portraits and cross section of the basin of attraction. Hardware experiments and Pspice-based circuit simulations are included in order to support numerical simulations. To our knowledge, such phenomena have not yet been reported in this oscillator and therefore constitute a significant contribution in understanding of the dynamical behavior of this type of oscillators and their potential applications.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020