Influence of Φ 4 and Φ 6 potentials on the synchronization of chaotic systems: a comparative study

The synchronization of dynamical systems is a well-documented phenomenon across scientific disciplines including biology, optics, and engineering. Classical chaotic systems like the Duffing, van der Pol, and Rayleigh oscillators exhibit enhanced dynamics when their potential functions are modified, where polynomial potentials of varying degrees and symmetry properties significantly influence both system behavior and synchronization characteristics. This numerical study analyzes a master–slave system comprising a van der Pol oscillator with Φ 4 potential (master) coupled to a Rayleigh–Duffing oscillator (slave), investigating how Φ 4 and Φ 6 potentials affect complete synchronization through temporal average comparisons of gyroscopic, dissipative, elastic, and hybrid coupling methods. Results demonstrate that the Φ 6 potential provides superior position-difference minimization, with optimal synchronization achieved through a combined gyroscopic–dissipative–elastic coupling scheme, as quantitatively verified by solution plots of the synchronization dynamics.