AN ANALOG COMPUTER STUDY OF VAN DER POL'S EQUATION AND ITS RESPONSE TO WHITE GAUSSIAN NOISE

摘要

Van der Pol's equation has a nonlinearity in the first derivative term and characteristics of the equation vary with a constant in the nonlinear term. Results of a computer study of the homogeneous equation compare favorably with phase plane data and periods obtained by numerical methods. Computer analysis of responses to random excitation show that the rms decreases exponentially toward the rms of the unexcited system as the constant in the nonlinear term is increased for constant noise input. Frequencies of the excited response become more random as excitation spectral density is increased but the pre-dominant frequency is the same as for the homogeneous equation.