This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network top...This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the assortative property of the network affects synchronization.展开更多
Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also ...Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also eventually dissipative under the hypothesis of eventual dissipation of the uncoupled oscillators. And the dynamics of the network is analyzed in its absorbing domain by combining two methods developed recently. Suufficient conditions for synchronization in the oscillator networks with nonlinear coupling are obtained. The two methods are combined effectively and the results embody the respective merits of the two methods. Numerical simulations confirm the validity of the results.展开更多
Cell division must be tightly coupled to cell growth in order to maintain cell size,whereas the mechanisms of how initialization of mitosis is regulated by cell size remain to be elucidated.We develop a mathematical m...Cell division must be tightly coupled to cell growth in order to maintain cell size,whereas the mechanisms of how initialization of mitosis is regulated by cell size remain to be elucidated.We develop a mathematical model of the cell cycle,which incorporates cell growth to investigate the dynamical properties of the size checkpoint in embryos of Xenopus laevis.We show that the size checkpoint is naturally raised from a saddle-node bifurcation,and in a mutant case,the cell loses its size control ability due to the loss of this saddle-node point.展开更多
By using AKNS[Phys.Rev.Lett.31(1973)125]system and introducing the wave function,a family of interesting exact solutions of the sine-Gordon equation are constructed.These solutions seem to be some soliton,kink,and.ant...By using AKNS[Phys.Rev.Lett.31(1973)125]system and introducing the wave function,a family of interesting exact solutions of the sine-Gordon equation are constructed.These solutions seem to be some soliton,kink,and.anti-kink ones respectively for the different choice of the spectrum,whereas due to the interaction between two traveling-waves they have some properties different from usual soliton,kink,and anti-kink solutions.展开更多
By combining the Backlund transformations and the AKNS system[Study in Appl.Math.53(1974)249.]which is a linear eigenvalue problem of the corresponding evolution equation,a method to find new exact solutions from know...By combining the Backlund transformations and the AKNS system[Study in Appl.Math.53(1974)249.]which is a linear eigenvalue problem of the corresponding evolution equation,a method to find new exact solutions from known stationary solutions for nonlinear integrable equations is proposed.As an example,Korteweg de Vries(KdV)equation is used to illustrate this method,and a class of new exact solutions of KdV equation is obtained.展开更多
基金The project supported by National Natural Science Foundation of China Under Grant Nos. 10672093, 10372054t and 70431002
文摘This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the assortative property of the network affects synchronization.
基金National Natural Science Foundation of China under Grant Nos.70431002 and 10672093
文摘Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also eventually dissipative under the hypothesis of eventual dissipation of the uncoupled oscillators. And the dynamics of the network is analyzed in its absorbing domain by combining two methods developed recently. Suufficient conditions for synchronization in the oscillator networks with nonlinear coupling are obtained. The two methods are combined effectively and the results embody the respective merits of the two methods. Numerical simulations confirm the validity of the results.
基金Supported by the National Natural Science Foundation of China under Grant No 10971152.
文摘Cell division must be tightly coupled to cell growth in order to maintain cell size,whereas the mechanisms of how initialization of mitosis is regulated by cell size remain to be elucidated.We develop a mathematical model of the cell cycle,which incorporates cell growth to investigate the dynamical properties of the size checkpoint in embryos of Xenopus laevis.We show that the size checkpoint is naturally raised from a saddle-node bifurcation,and in a mutant case,the cell loses its size control ability due to the loss of this saddle-node point.
基金Supported by the National Natural Science Foundation of China under Grant No.19872044.
文摘By using AKNS[Phys.Rev.Lett.31(1973)125]system and introducing the wave function,a family of interesting exact solutions of the sine-Gordon equation are constructed.These solutions seem to be some soliton,kink,and.anti-kink ones respectively for the different choice of the spectrum,whereas due to the interaction between two traveling-waves they have some properties different from usual soliton,kink,and anti-kink solutions.
基金Supported by the National Natural Science Foundation of China under Grant No.19872044.
文摘By combining the Backlund transformations and the AKNS system[Study in Appl.Math.53(1974)249.]which is a linear eigenvalue problem of the corresponding evolution equation,a method to find new exact solutions from known stationary solutions for nonlinear integrable equations is proposed.As an example,Korteweg de Vries(KdV)equation is used to illustrate this method,and a class of new exact solutions of KdV equation is obtained.
