Amplitude control and projective synchronization of a dynamical system with exponential nonlinearity

A dynamical system with exponential nonlinearity is reported in this paper. Analysis shows that one can flexibly control signal amplitude of the system by introducing control function in the exponential nonlinear term, and the corresponding Lyapunov exponents keep invariable. But the coefficient in cross-product term cannot provide amplitude modulation. By considering the fact that the unique amplitude function can provide the scale factors, a control scheme combining the techniques of linear feedback and variable substitution is presented to realize projective synchronization of the chaotic system.