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.
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