It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspond...It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspondence between the set of linearly recursive sequences of 1-index and F[X]° is generalized to the case of n-index.展开更多
We investigate the dynamics of two extensive classes of recursive sequences：Xn＋1 =c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）/c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… x...We investigate the dynamics of two extensive classes of recursive sequences：Xn＋1 =c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）/c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）and Xn＋1c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）/c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）We prove that their unique positive equilibrium 5 = 1 is globally asymptotically stable. And a new access is presented to study the theory of recursive sequences.展开更多
In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attr...In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attractive, also the attractive basin of the equilibrium is obtained.展开更多
In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on ce...In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.展开更多
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compu...In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.展开更多
In this paper, we investigate the global behavior of the difference equation xn＋1=1-2n/A＋∑k i=1xn-iwith the A ∈ （-∞,-1） is a real number, k is a positive integer and the initial conditions x_k x0 ∈ （-∞, 0].
In this paper we obtain sufficient conditions for the global asymptotic stabilityof the difference equationWe also apply our results to the rational recursive sequenceAMS No.: 39A12
In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonze...In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonzero real numbers.展开更多
文摘It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf algebras.By the way, the correspondence between the set of linearly recursive sequences of 1-index and F[X]° is generalized to the case of n-index.
基金Supported by the National Natural Science Foundation of China (Grant No10771169)
文摘We investigate the dynamics of two extensive classes of recursive sequences：Xn＋1 =c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）/c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）and Xn＋1c∑j=1^k（i0,i1,…,i2j-1）∈A2j-1∑ xn-i0xn-i1… xn-i2j-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2k）/c∑j=0^k（i0,i1…,i2j）∈A2j ∑xn-i0xn-i1… xn-i2j＋.f（xn-i0, xn-i1,..., xn-i2k）We prove that their unique positive equilibrium 5 = 1 is globally asymptotically stable. And a new access is presented to study the theory of recursive sequences.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical and Astronautical University
文摘In this paper, we investigate the global behavior of a recursive sequence. We get sufficient conditions for the existence of the unique equilibrium point, and the unique equilibrium point is proved to be globally attractive, also the attractive basin of the equilibrium is obtained.
文摘In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.
文摘In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.
文摘In this paper, we investigate the global behavior of the difference equation xn＋1=1-2n/A＋∑k i=1xn-iwith the A ∈ （-∞,-1） is a real number, k is a positive integer and the initial conditions x_k x0 ∈ （-∞, 0].
文摘In this paper we obtain sufficient conditions for the global asymptotic stabilityof the difference equationWe also apply our results to the rational recursive sequenceAMS No.: 39A12
文摘In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonzero real numbers.
