A RD dynamic competition model with spillover effects is established in the rent-seeking framework. The local stability analysis is firstly conducted, evolutionary properties of the system restricted to two axes, which are the basic boundaries of feasible sets, are then analyzed and the whole boundary of feasible sets is determined. Global properties of systems with symmetrical and nonsymmetrical structure are studied. Under some conditions, several attractors may coexist, even chaos attractor and periodic attractor may coexist. The multi-stability makes the system＇s dynamic behavior sensitive to initial conditions, that is to say, different initial conditions may lead the dynamic pro- cess to basin of different attractors. At last, the competing states are analyzed under different parameter conditions