Abstract
Conditions are given which preclude the existence of a nontrivial periodic orbit for a difference equation in ℝn. The conditions are analogous to those of Bendixson and Dulac for autonomous planar differential equations.
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McCluskey, C.C., Muldowney, J.S. Bendixson-Dulac Criteria for Difference Equations. Journal of Dynamics and Differential Equations 10, 567–575 (1998). https://doi.org/10.1023/A:1022677008393
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DOI: https://doi.org/10.1023/A:1022677008393