In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that ...In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that of coefficients of the linear part. Under some parametric conditions, the system can produce chaotic attractors similar as Lorenz attractor. A constructive theorem is proposed for generalized synchronization related to the fractional-order chaotic system and an application of this new system is demonstrated.展开更多
The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) descr...The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.展开更多
基金Supported by the National Nature Science Foundation of China under Grant No.60674059
文摘In this paper a new dynamic system with integer and fractional order is investigated. It is shown that determining the effect of quadratic coefficients to the systematic structure can be converted to determining that of coefficients of the linear part. Under some parametric conditions, the system can produce chaotic attractors similar as Lorenz attractor. A constructive theorem is proposed for generalized synchronization related to the fractional-order chaotic system and an application of this new system is demonstrated.
基金supported by the National Natural Science Foundation of China (Grant No. 11002029)
文摘The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.
