Dinâmica não linear de osciladores de van der pol acoplados

Abstract

Coupled Van der Pol equations may serve as a basis for mathematical modeling of various systems in physics, biology, and medicine. Therefore, this work seeks to investigate the dynamic behavior of coupled Van der Pol oscillators under different external excitation conditions, with an emphasis on numerical analysis of the system. For this purpose, four different situations were considered: absence of external excitation, constant excitation, harmonic excitation, and non-ideal excitation. The primary objective is to understand the influence of these configurations on the system’s dynamics, specifically regarding periodic and chaotic responses. To accomplish this, bifurcation diagrams, phase portraits, color matrices, and time series analyses were employed, facilitating the identification of both the presence and breakdown of symmetry across different scenarios. The findings demonstrate that the application of external excitations may results a range of complex behaviors, which may be explored in applications.