We investigate the long-term behavior of solutions of the difference equation $$x_{n+1}=x_{n}x_{n-3}-1, n=0,1, \ldots $$ where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.
Kent, C. M. & Kosmala, W. (2011). On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$. International Journal of Nonlinear Analysis and Applications, 2(2), 24–43. https://doi.org/10.22075/ijnaa.2011.91
MLA
Kent, C. M., & Kosmala, W. "On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$", International Journal of Nonlinear Analysis and Applications, 2, 2, 2011, 24–43. doi: 10.22075/ijnaa.2011.91
HARVARD
Kent, C. M., & Kosmala, W. (2011). 'On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$', International Journal of Nonlinear Analysis and Applications, 2(2), pp. 24–43. doi: 10.22075/ijnaa.2011.91
CHICAGO
Kent, C. M. & Kosmala, W., "On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$." International Journal of Nonlinear Analysis and Applications, 2 2 (2011): 24–43, doi: 10.22075/ijnaa.2011.91
VANCOUVER
Kent C. M., Kosmala W. On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$. IJNAA. 2011;2(2):24–43. doi: 10.22075/ijnaa.2011.91
International Journal of Nonlinear Analysis and Applications