A dynamical model of a nonlinear oscillator of a single degree of freedom is presented.The structure of the model is constructed by a positive stiffness component and a pair of inclined linear springs providing negative stiffness, which is of geometrical nonlinear configuration.The system subjected to harmonic excitations is investigated for all kinds of parameters, where lots of nonlinear dynamical phenomena and their existence law are found and some bifurcations as well as their formation mechanism are made out.Lots of numerical simulations are carried out by using of types of dynamics theoreties, such as Runge-Kutta method, Floquent Theory, Lyapunov exponent, manifold analysis etc.In this paper the comprehensive results are presented to provide a better understanding for the complicated dynamics of low frequency nonlinear system.