In order to control the amplitude of a limit cycle of a coupled van der Pol system, feedback controllers are designed; the control equations of weakly nonlinear systems are obtained by using an approximate method and the relationship between the amplitude of the limit cycle and the control parameter is acquired. Hence the amplitude of the limit cycle can be controlled effectively. The method may also be applied to other coupled van der Pol systems. For some systems, it is difficult to find the function in the amplitude of the limit cycle and the control parameter directly. By means of numerical analysis, we can design effective controllers; therefore we can preferentially control the amplitude of the limit cycle of coupled van der Pol systems.

This paper suggests an approach to solve the generalized Benjamin-Bona-Mahony (BBM) equation. The approach is given through improving the tanh function method based on an auxiliary ordinary differential equation, and is used to construct explicit traveling wave solutions of nonlinear evolution equations. We will show the efficiency of our method through the generalized BBM equation. The results we have got in the present paper indicate that our approach not only offers the existing solutions in literature, but also some new solitary wave solutions and triangular periodic wave solutions.