Nkashama, M. N.2020-01-062020-01-062000-01-01Nkashama, M. N. (2000). Dynamics of logistic equations with non-autonomous bounded coefficients. <i>Electronic Journal of Differential Equations, 2000</i>(02), pp. 1-8.1072-6691https://hdl.handle.net/10877/9132We prove that the Verhulst logistic equation with positive non-autonomous bounded coefficients has exactly one bounded solution that is positive, and that does not approach the zero-solution in the past and in the future. We also show that this solution is an attractor for all positive solutions, some of which are shown to blow-up in finite time backward. Since the zero-solution is shown to be a repeller for all solutions that remain below the afore-mentioned one, we obtain an attractor-repeller pair, and hence (connecting) heteroclinic orbits. The almost-periodic attractor case is also discussed. Our techniques apply to the critical threshold-level equation as well.Text8 pages1 file (.pdf)enAttribution 4.0 InternationalNon-autonomous logistic equationThreshold-level equationPositive and bounded solutionsComparison techniquesω-limit pointsMiximal and minimal bounded solutionsAlmost-periodic functionsSeparated solutionsArticle