https://doi.org/10.1140/epjp/s13360-022-02981-4
Regular Article
Dynamic analysis of a memristive diode bridge-based higher order autonomous Van der Pol-Duffing oscillator
1 Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
2 Unité de Recherche de Matière Condensée, d’Electronique et de traitement de signal (UR-MACETS), Department of Physics, University of Dschang, Dschang, Cameroon
3 Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon
Received:
19
February
2022
Accepted:
21
June
2022
Published online: 8 July 2022
It is known that hyperchaotic signals are suited for designing chaos-based secure communication systems. Based on a first-order generalized diodes bridge memristor emulator, the dynamical behavior of a higher order autonomous Van der Pol-Duffing oscillator is investigated in this article. This oscillator is able to exhibit some complex and interesting behaviors (chaos, hyperchaos and multistability) suitable to improve secure communications. The analysis of the equilibriums points and is performed. Well-known standard nonlinear tools such as Lyapunov exponents spectra, bifurcation diagrams and phase space trajectories plots shows that the system generates some complex nonlinear phenomena including period doubling route to chaos and then to hyperchaos through boundary condition, with the variation of control parameter. More interestingly, a window of hysteretic dynamics (coexistence of multiple attractors) and a hidden attractor are observed in some regions of the parameter space depending solely on the choice of initial states. The cross sections of the basin of attraction obtained for the same set of parameters are shown and display complex basin boundaries thus suggesting possible jumps between coexisting solutions in experiment. PSpice simulation results are carried out to verify its physical existence.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022