This paper studies the nonlinear vibration of a dielectric elastomer balloon considering both the strain-stiffening and the second invariant of the Cauchy-Green deformation tensor. To this end, the Gent-Gent hyperelastic model is proposed. The ordinary differential equation governing the motion of the system is derived using the Euler-Lagrange energy method. Then, it is solved with the application of a time integration-based solver. The chaotic interval for critical system parameters is identified, with and without considering the influence of the second invariant. This identification is conducted by depicting bifurcation diagrams of Poincaré sections and the largest Lyapunov exponent criteria. In order to better analyse different motions of the system, time histories, phase-plane diagrams, Poincaré maps, and power spectral densities are illustrated. Based on the obtained results, the second invariant parameter of the Gent-Gent model could suppress the chaotic motion of the system. Increasing this parameter, a transition from the chaos to the quasiperiodic attractor would happen.
