Qualitative Properties of Difference Equation of Order Six
Abstract
:1. Introduction
- (i)
- The equilibrium point of Equation (1.2) is locally stable if for every there exists such that for all ,with
- (ii)
- The equilibrium point of Equation (1.2) is locally asymptotically stable if is locally stable solution of Equation (1.2) and there exists such that for all , with
- (iii)
- The equilibrium point of Equation (1.2) is global attractor if for all , we have
- (iv)
- The equilibrium point of Equation (1.2) is globally asymptotically stable if is locally stable, and is also a global attractor of Equation (1.2).
- (v)
- The equilibrium point of Equation (1.2) is unstable if is not locally stable.
- (vi)
- The linearized equation of Equation (1.2) about the equilibrium is the linear difference equation
- (a)
- is non-decreasing in for each fixed and is non-increasing in for each fixed
- (b)
- For any that is a solution of the system
2. Local Stability of the Equilibrium Point of Equation (1.1)
3. Global Attractivity of the Equilibrium Point of Equation (1.1)
4. Boundedness of Solutions of Equation (1.1)
5. Special Cases of Equation (1.1)
5.1. First Equation
5.2. Second Equation
5.3. Third Equation
5.4. Fourth Equation
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Khaliq, A.; Elsayed, E.M. Qualitative Properties of Difference Equation of Order Six. Mathematics 2016, 4, 24. https://doi.org/10.3390/math4020024
Khaliq A, Elsayed EM. Qualitative Properties of Difference Equation of Order Six. Mathematics. 2016; 4(2):24. https://doi.org/10.3390/math4020024
Chicago/Turabian StyleKhaliq, Abdul, and E.M. Elsayed. 2016. "Qualitative Properties of Difference Equation of Order Six" Mathematics 4, no. 2: 24. https://doi.org/10.3390/math4020024
APA StyleKhaliq, A., & Elsayed, E. M. (2016). Qualitative Properties of Difference Equation of Order Six. Mathematics, 4(2), 24. https://doi.org/10.3390/math4020024