This paper introduces the complex Rayleigh-van der Pol-Duffing oscillators (RVDOs), which are hyperchaotic and can be either autonomous or non-autonomous. The fundamental dynamics of the autonomous and nonautonomous complex RVDOs including dissipation, symmetry, fixed points and their stability are studied. These oscillators are found in various important fields of physics and engineering. The paper proposes a scheme to achieve phase synchronization (PS) and antiphase synchronization (APS) for different dimensional models. These kinds of synchronization are considered as generalization of several other types of synchronization. For this scheme we use the active control method based on Lyapunov stability theory. By analytically determining the control functions, the scheme achieved PS and APS. Our scheme is applied to study PS of hyperchaotic behaviours
for two distinct hyperchaotic non-autonomous and autonomous complex RVDOs. Additionally, the scheme is employed to achieve APS of chaotic real non-autonomous RVDO and hyperchaotic complex
autonomous RVDO, including those with different dimensions. Our work presents numerical results that plot the amplitudes and phases of these hyperchaotic behaviours, demonstrating the successful achievement of PS and APS.
Keywords
hyperchaotic; complex; Rayleigh-Van der Pol-duffing oscillator; phase synchronization; anti phase synchronization
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
