Abstract
The second-order difference equation , where 0<a<1, 0<b and 0<c<1, has been used to model the generations of the perennial grass Agrostis scabra. The permanence of the solutions was proved. For certain parameter values in this model, and in the data from field studies, chaotic dynamics was conjectured. In this study, with the aid of a homoclinic shadowing theorem, we prove the existence of a transversal homoclinic orbit, hence the presence of chaotic dynamics, for certain parameter values of this second-order difference equation.
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