Abstract
We present some comments on the behavior of solutions of the difference equation \(x_{n + 1} = p_k x_n + p_{k - 1} x_{n - 1} + \ldots + p_1 x_{n - k + 1} ,{\text{ }}n = - 1,0,1 \ldots ,\)where p i ≥ 0, i = 1,..., k, k ∈ N, and x −k ,..., x −1 ∈ R.
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REFERENCES
D. Ya. Khusainov and S. N. Nikiforova, “Stability of a difference equation with positive coefficients,” Ukr. Mat. Zh., 51, No. 9, 1276-1280 (1999).
E. C. Pielou, An Introduction to Mathematical Ecology, Wiley, New York (1969).
E. C. Pielou, Population and Community Ecology, Gordon and Breach, New York (1974).
R. J. Beddington and S. J. Holt, “On the dynamics of exploited fish populations,” Fish. Invest. London, 19, 1-53 (1957).
R. C. de Vault, G. Dial, V. L. Kocic, and G. Ladas, “Global behaviour of solution of x n?1 = ax n ??f (xn , xn-1 ),” J. Different. Equat. Appl., 4, 311-330 (1998).
M. E. Fisher and B. S. Goh “Stability results for delayed-recruitment models in population dynamics,” J. Math. Biol., 19, 147-156 (1984.).
E. A. Grove, C. M. Kent, G. Ladas, and S. Valicenti, “Global stability in some population models,” in: Proc. Forth Int. Conf. Different. Equat. and Appl. (August 27-31, 1999, Poznan, Poland), Gordon and Breach, New York (2000), pp. 149-176.
R. C. de Vault, E. A. Grove, G. Ladas, R. Levins, and C. Puccia, “Oscillations and stability in a delay model of perennial grass,” J. Different. Equat. Appl., 1, 173-185 (1995).
J. M. Cushing and Y. Kuang, “Global stability in a nonlinear difference delay equation model of flour beetle population growth,” J. Different. Equat. Appl., 2, 31-37 (1996).
H. Sedaghat, “Geometric stability conditions for higher order difference equations,” J. Math. Anal. Appl., 224, 255-272 (1998).
S. Stevi?, “A global convergence result,” Indian J. Math. (to appear).
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Stević, S. A Note on the Recursive Sequence x n + 1 = p k x n + p k − 1 x n − 1 +...+ p 1 x n − k + 1 . Ukrainian Mathematical Journal 55, 691–697 (2003). https://doi.org/10.1023/B:UKMA.0000010169.93540.c2
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DOI: https://doi.org/10.1023/B:UKMA.0000010169.93540.c2