A differential-difference Davey-Stewartson system with self-consistent sources is constructed using the source generation procedure. We observe how the resulting coupled discrete system reduces to the identities for d...A differential-difference Davey-Stewartson system with self-consistent sources is constructed using the source generation procedure. We observe how the resulting coupled discrete system reduces to the identities for determinant by presenting the Gram-type determinant solution and Casorati-type determinant solution.展开更多
The integrable hungry Lotka-Volterra （hLV） system stands for a prey-predator model in mathematical biology. The discrete-time hLV （dhLV） system is derived from a time discretization of the hLV system. The solution...The integrable hungry Lotka-Volterra （hLV） system stands for a prey-predator model in mathematical biology. The discrete-time hLV （dhLV） system is derived from a time discretization of the hLV system. The solution to the dhLV system is known to be represented by using the Casorati determinant. In this paper, we show that if the entries of the Casorati determinant become an extended Fibonacci sequence at the initial discrete time, then those are also an extended Fibonacci sequence at any discrete time. In other words, the extended Fibonacci sequence always appears in the entries of the Casorati determinant under the time evolution of the dhLV system with suitable initial setting. We also show that one of the dhLV variables converges to the ratio of two successive extended Fibonacci numbers as the discrete time goes to infinity.展开更多
基金National Natural Science Foundation of China(11301454,11271168)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(13KJD110009)+1 种基金the Jiangsu Qing Lan Project for Excellent Young Teachers in University(2014)XZIT(XKY 2013202)
基金Research supported by the National Natural Science Foundation of China(11301454,11271168)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(13KJD110009)
文摘A differential-difference Davey-Stewartson system with self-consistent sources is constructed using the source generation procedure. We observe how the resulting coupled discrete system reduces to the identities for determinant by presenting the Gram-type determinant solution and Casorati-type determinant solution.
文摘The integrable hungry Lotka-Volterra （hLV） system stands for a prey-predator model in mathematical biology. The discrete-time hLV （dhLV） system is derived from a time discretization of the hLV system. The solution to the dhLV system is known to be represented by using the Casorati determinant. In this paper, we show that if the entries of the Casorati determinant become an extended Fibonacci sequence at the initial discrete time, then those are also an extended Fibonacci sequence at any discrete time. In other words, the extended Fibonacci sequence always appears in the entries of the Casorati determinant under the time evolution of the dhLV system with suitable initial setting. We also show that one of the dhLV variables converges to the ratio of two successive extended Fibonacci numbers as the discrete time goes to infinity.
