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
Frequency combs show various applications in molecular fingerprinting,imaging,communications,and so on.In the terahertz frequency range,semiconductor-based quantum cascade lasers(QCLs)are ideal platforms for realizing...Frequency combs show various applications in molecular fingerprinting,imaging,communications,and so on.In the terahertz frequency range,semiconductor-based quantum cascade lasers(QCLs)are ideal platforms for realizing the frequency comb operation.Although self-started frequency comb operation can be obtained in free-running terahertz QCLs due to the four-wave mixing locking effects,resonant/off-resonant microwave injection,phase locking,and femtosecond laser based locking techniques have been widely used to broaden and stabilize terahertz QCL combs.These active locking methods indeed show significant effects on the frequency stabilization of terahertz QCL combs,but they simultaneously have drawbacks,such as introducing large phase noise and requiring complex optical coupling and/or electrical circuits.Here,we demonstrate Farey tree locking of terahertz QCL frequency combs under microwave injection.The frequency competition between the Farey fraction frequency and the cavity round-trip frequency results in the frequency locking of terahertz QCL combs,and the Farey fraction frequencies can be accurately anticipated based on the downward trend of the Farey tree hierarchy.Furthermore,dual-comb experimental results show that the phase noise of the dual-comb spectral lines is significantly reduced by employing the Farey tree locking method.These results pave the way to deploying compact and low phase noise terahertz frequency comb sources.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 Innovation Program for Quantum Science and Technology(2023ZD0301000)the National Science Fund for Distinguished Young Scholars(62325509)+2 种基金the National Natural Science Foundation of China(62235019,61875220,61927813,61991430,62035005,62105351,and 62305364)the“From 0 to 1”Innovation Program of the Chinese Academy of Sciences(ZDBS-LY-JSC009)the CAS Project for Young Scientists in Basic Research(YSBR-069).
文摘Frequency combs show various applications in molecular fingerprinting,imaging,communications,and so on.In the terahertz frequency range,semiconductor-based quantum cascade lasers(QCLs)are ideal platforms for realizing the frequency comb operation.Although self-started frequency comb operation can be obtained in free-running terahertz QCLs due to the four-wave mixing locking effects,resonant/off-resonant microwave injection,phase locking,and femtosecond laser based locking techniques have been widely used to broaden and stabilize terahertz QCL combs.These active locking methods indeed show significant effects on the frequency stabilization of terahertz QCL combs,but they simultaneously have drawbacks,such as introducing large phase noise and requiring complex optical coupling and/or electrical circuits.Here,we demonstrate Farey tree locking of terahertz QCL frequency combs under microwave injection.The frequency competition between the Farey fraction frequency and the cavity round-trip frequency results in the frequency locking of terahertz QCL combs,and the Farey fraction frequencies can be accurately anticipated based on the downward trend of the Farey tree hierarchy.Furthermore,dual-comb experimental results show that the phase noise of the dual-comb spectral lines is significantly reduced by employing the Farey tree locking method.These results pave the way to deploying compact and low phase noise terahertz frequency comb sources.
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.
