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《Journal of Guangxi Normal University(Natural Science Edition)》 2017-01
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Global Asymptotic Stability of a Class of Difference Equations

HAN Caihong;LI Lüe;HUANG Lili;College of Mathematics and Statistics,Guangxi Normal University;  
In this paper,the global characteristics of the following difference equations are investigated:x_(n+1)=∑t i=1a_ix_(n-m_i)/(q+∑t i=1c_ix_(n-m_i)+∑s k=1 b_kx_(n-n_k)).Let A=∑t i=1a_i,B=∑s k=1 b_k,C=∑t i=1 c_i and l=max{m_t,n_s},where a_i0,c_i 0 for all 1≤i≤t,b0 for all 1≤k≤s,qA,B≠C,0≤m_1m_2…m_t,,0≤n_1n_2…n_s,and {m_1,m_2,…,m_t }∩{n_1,n_2,…,n_s} =?,and the initial values are positive.By constructing a suitable system o{ equations and binary {unctions,it is proved that the unique equilibrium solution of the equation is locally stable and a global attractor.In other words,the solution is globally asymptotically stable.
【Fund】: 国家自然科学基金(11461007);; 广西区高校中青年教师基础能力提升项目(KY2016YB069);; 广西壮族自治区大学生创新创业培训计划项目(201610602186)
【CateGory Index】: O175.7
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