In this paper, a distributed stabilization problem is investigated for heterogeneous agents in the strong-weak competition network which contains three kinds of relationships between agents: cooperation, strong competition and weak competition, and all the agents are governed by the second-order systems with different intrinsic dynamics. The whole network satisfies the structural balance which can be divided into two sub-networks, while strong and weak competitions are alternate action on the agents from different sub-networks. Then, the switched system approach is first proposed to study the distributed stabilization problem, which is found that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced, and several effective sufficient conditions are attained. Furthermore, it is shown that the condition on the periodical switching law is less conservative when each subsystem can only be activated once within one period. Finally, these theoretical results are demonstrated by the numerical simulations.