Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function
Abstract
:1. Introduction
2. Global Behavior
2.1. Classification of Solutions
- (i)
- eventually equals c, more precisely , which occurs when for some ;
- (ii)
- is eventually less than c, more precisely , , which occurs when for some ; or
- (iii)
- oscillates about c with at most consecutive decreasing terms greater than c and at most k consecutive increasing terms less than c.
2.2. Global Asymptotic Stability
2.3. Illustrative Examples
3. Concluding Remarks
Acknowledgments
Conflicts of Interest
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Ma, W.-X. Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function. Mathematics 2020, 8, 825. https://doi.org/10.3390/math8050825
Ma W-X. Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function. Mathematics. 2020; 8(5):825. https://doi.org/10.3390/math8050825
Chicago/Turabian StyleMa, Wen-Xiu. 2020. "Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function" Mathematics 8, no. 5: 825. https://doi.org/10.3390/math8050825
APA StyleMa, W.-X. (2020). Global Behavior of an Arbitrary-Order Nonlinear Difference Equation with a Nonnegative Function. Mathematics, 8(5), 825. https://doi.org/10.3390/math8050825