Nonlinear response of a harmonically driven oscillator in magnetic field

Abstract

The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaotically between different equilibrium positions. To prove this result, Lyapunov exponents have been calculated using the algorithm proposed by Rangarajan G., Habib S. and Ryne R.: Physical Review Letters, vol. 80, (1998). Moreover, the appropriate time series, phase portrait, Poincar'e cross-section and power spectrum are given to support the conclusion