An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations

Abstract

In this work, a master–slave system composed by a pair of damped Duffing oscillators with variable coefficients and nonlinear coupling is investigated. An integral of motion for the system is obtained using a symmetry transformation and Noether’s theorem. Some numerical examples are presented for different cases of damping and oscillation frequency, for a varying coupling constant. The system dynamics is studied by means of space-time surfaces, time series and phase portraits. For a constant oscillation frequency, the slave presents envelopes that tend to become chaotic as the coupling constant increases. Meanwhile, as the frequency increases with time, the slave has higher amplitudes and speeds than the master oscillator.