Dynamical Behavior of Oscillators Models with Sine Nonlinearity

Abstract

This work is devoted to the dynamic behavior of two models of nonlinear oscillators with sine nonlinearity. In this work the potential energy is considered as the derivative of the sine function and given by (1/e*d)*((sin^n(x))*((sin^n(x))+e)*((sin^n(x))+d)). A study of these oscillators in their self-sustaining and forced state is made, and we observe an important frequency variation. To explain this frequency variation, with the help of mathematical developments, the limit to which sin(x) can approach was considered. This allowed us to obtain the nonlinear algebraic equations and the frequency ranks for which the models are trained in frequencies. The models present a very rich dynamic characterized by the presence of periodical regions of stability and instability. Contrary to the classic case, the sinus function brings large chaotic zones. We also observe that these models can play with some approximations the role of artificial pacemaker. Experimental realization being difficult with the presence of the analog sines, an experimental simulation by ATmega328P microcontroller was carried out. There is good agreement between digital simulation and microcontroller.