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一类高阶有理差分方程的动力学定理

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根据差分方程理论,证明了高阶有理差分方程xn+1=A+Bxn/3的5个动力学定理,即唯一的正平衡解x的局部渐近稳定性、全局渐近稳定性、有界性、持续性、周期解与半循环长度等不同结论.并用计算机Matlab程序描绘此差分方程解的图像,进一步验证了这5个定理.
DYNAMICAL THEOREMS FOR A CLASS OF HIGHER ORDER RATIONAL DIFFERENCE EQUATIONS
According to the theory of difference equations,we prove five dynamic theorems for rational difference equations xn+1=A+Bxn/xn-m3,including locally asymptotically stability,global asymptotically stability,boundedness,persistence,periodic solution,and semi-cycle length of the unique positive equilibrium solution.Then we used Matlab's numerical calculations to obtain the graph of the solution to the difference equation,which more intuitively verified the correctness of these 5 theorems.

difference equationequilibrium pointasymptotically stableboundednesssemi-cycle length

全卫贞、王丽、周敬人、黄日娣、刘付滢、吴语桐、胡可满

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湛江幼儿师范专科学校数学系,广东,湛江 524037

岭南师范学院基础教育学院,广东,湛江 524037

差分方程 平衡解 渐近稳定性 有界性 半循环长度

2024

井冈山大学学报(自然科学版)
井岗山大学

井冈山大学学报(自然科学版)

影响因子:0.298
ISSN:1674-8085
年,卷(期):2024.45(4)