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On the Behavior of Positive Solutions of a Difference Equations System x<sub>n+1</sub>={y<sub>n-2</sub>+y<sub>n-3</sub>}/x<sub>n</sub>, y<sub>n+1</sub>={x<sub>n-2</sub>+x<sub>n-3</sub>}/y<sub>n</sub>
Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
- 1 Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
- 2 Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
- 3 Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
- 4 Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University Yantai, Yantai, China
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Abstract
Motivated by an open problem in the literature “Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture”, we introduce a difference equation system: x n+1 ={y n-2 +y n-3 }/x n , y n+1 ={x n-2 +x n-3 }/y n , n=o, 1 ...* Where x i, y i ∈（0, ∞）， i=-3, -2, -1, 0. We try to find out some conditions such that the solution of system converges to periodic solution. This model can be applied to the two species competition and population biology.
KeywordsDifference EquationSystemMonotonicityPeriodicityOscillatory
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