ymmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network （WTN） has been rarely studied so far. In this paper, the auth...ymmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network （WTN） has been rarely studied so far. In this paper, the authors systematically explore the symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.展开更多
A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreove...A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 70371070 Shanghai Leading Academic Discipline Project under Grant No. S30504Key Project for Fundamental Research of STCSM under Grant No. 06JC14057
文摘ymmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network （WTN） has been rarely studied so far. In this paper, the authors systematically explore the symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.
基金Supported by the Natural Science Foundation of China under Grant No.11061028
文摘A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.
