Chatterjee, Esha and Hassan, Sk Sarif (2018) ON THE ASYMPTOTIC CHARACTER OF A GENERALIZED RATIONAL DIFFERENCE EQUATION. In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38 (4). pp. 1707-1718.
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We investigate the global asymptotic stability of the solutions of Xn+1 = beta Xn-l+gamma Xn-k/A+Xn-k for n = 1, 2, ..., where 1 and k are positive integers such that l not equal k. The parameters are positive real numbers and the initial conditions are arbitrary nonnegative real numbers. We find necessary and sufficient conditions for the global asymptotic stability of the zero equilibrium. We also investigate the positive equilibrium and find the regions of parameters where the positive equilibrium is a global attractor of all positive solutions. Of particular interest for this generalized equation would be the existence of unbounded solutions and the existence of prime period two solutions depending on the combination of delay terms (l, k) being (odd, odd), (odd, even), (even, odd) or (even, even). In this manuscript we will investigate these aspects of the solutions for all such combinations of delay terms.
| Item Type: | Journal Article |
|---|---|
| Publication: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS |
| Publisher: | AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA |
| Additional Information: | Copyright of this article belong to AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 13 Aug 2018 15:31 |
| Last Modified: | 13 Aug 2018 15:31 |
| URI: | http://eprints.iisc.ac.in/id/eprint/60411 |
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