In this paper , through the discrim ination of Farey sequence in the forced Brusselator withweak coupling , it is proved that there is a topological translation fro m a nonlinear differen tial system ( limit cycle)...In this paper , through the discrim ination of Farey sequence in the forced Brusselator withweak coupling , it is proved that there is a topological translation fro m a nonlinear differen tial system ( limit cycle) to the circle m ap .展开更多
In this paper, we introduce Farey triangle graph , Farey triangle matrix , complementary Farey triangle graph and complementary Farey triangle matrix , and we derive some properties of the following matrices.
Cascading failure is an important part of the dynamics in complex network.In this paper,we research the cascading failure of Farey network which is scale-free network with fractal properties by data analysis.According...Cascading failure is an important part of the dynamics in complex network.In this paper,we research the cascading failure of Farey network which is scale-free network with fractal properties by data analysis.According to the analyses,we obtain an iterative expression of the failure nodes’number at the certain time step,anther iterative expression of the time which is needed for the network being global collapse,and the sequence of nodes failure in the Farey network.By theoretical derivation,we get an approximate solutions of perturbation threshold R to make the network achieve the global collapse.If the nodes number of the Farey network is lager,simulate results are closer to theoretical value.By the simulation,we obtain the cascading failure process of the Farey network after suffering deliberate attack and random attack.Simulation results show that,the failure nodes of Farey network increase gradually as R raises,until the network is global collapse.Moreover,Farey network shows stronger robustness for random attack.abstract environment.展开更多
Generalized Farey tree network （GFTN） and generalized Farey organized pyramid network （CFOPN） model are proposed, and their topological characteristics are studied by both theoretical analysis and numerical simula...Generalized Farey tree network （GFTN） and generalized Farey organized pyramid network （CFOPN） model are proposed, and their topological characteristics are studied by both theoretical analysis and numerical simulations, which are in good accordance with each other. Then weighted GFTN is studied using cumulative distributions of its Farey number value, edge weight, and node strength. These results maybe helpful for future theoretical development of hybrid models.展开更多
文摘In this paper , through the discrim ination of Farey sequence in the forced Brusselator withweak coupling , it is proved that there is a topological translation fro m a nonlinear differen tial system ( limit cycle) to the circle m ap .
文摘In this paper, we introduce Farey triangle graph , Farey triangle matrix , complementary Farey triangle graph and complementary Farey triangle matrix , and we derive some properties of the following matrices.
文摘Cascading failure is an important part of the dynamics in complex network.In this paper,we research the cascading failure of Farey network which is scale-free network with fractal properties by data analysis.According to the analyses,we obtain an iterative expression of the failure nodes’number at the certain time step,anther iterative expression of the time which is needed for the network being global collapse,and the sequence of nodes failure in the Farey network.By theoretical derivation,we get an approximate solutions of perturbation threshold R to make the network achieve the global collapse.If the nodes number of the Farey network is lager,simulate results are closer to theoretical value.By the simulation,we obtain the cascading failure process of the Farey network after suffering deliberate attack and random attack.Simulation results show that,the failure nodes of Farey network increase gradually as R raises,until the network is global collapse.Moreover,Farey network shows stronger robustness for random attack.abstract environment.
基金supported by the Nature Science Foundation of China under Grand Nos. 70431002, 60874087, 60773120, and 10647001the Nature Science Foundation of Beijing under Grand No. 4092040
文摘Generalized Farey tree network （GFTN） and generalized Farey organized pyramid network （CFOPN） model are proposed, and their topological characteristics are studied by both theoretical analysis and numerical simulations, which are in good accordance with each other. Then weighted GFTN is studied using cumulative distributions of its Farey number value, edge weight, and node strength. These results maybe helpful for future theoretical development of hybrid models.
