In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
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Key Findings & Data:In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
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Conclusion & Impact:In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotic Stability · Difference Equation · Global Behavior
Abstract
In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.
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