摘要
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.
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
Supported by the National Natural Science Foundation of China (Grant No10771169)
