Measuring Chaotic Noise in Nonlinear Models

In many applications such as fluid or solid modeling, chaotic noise may be cumbersome. Instead of estimating the Lyapunov exponent of the system, one may be interested in measuring the amplitude of the system’s chaotic noise in a unit better suited to the application, e.g., the amplitude (in mm) of the vibration of a solid’s surface. The goal of this study is to propose a method to achieve this goal. The techniques are tested on a nonlinear biomechanical model of the face driven by muscle activity and a jaw hinge. The proposed method is effective and shows that (i) the amplitude of chaotic noise perceivable as skin vibration is approximately equal to 10% of the amplitude of a full-scale movement; (ii) the noise properties are similar in the stationary and dynamic states; (iii) the noise comes only from the skin model, not from the nonlinear muscle models. The method is simple and inexpensive to implement. It can therefore be useful in applications such as video animation or motor control research, where estimating the component of chaotic noise is more important than fully characterizing the nonlinear properties of a model.