Dynamics of Logistic Equations with Non-autonomous Bounded Coefficients

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dc.contributor.authorNkashama, M. N.
dc.date.accessioned2020-01-06T17:49:37Z
dc.date.available2020-01-06T17:49:37Z
dc.date.issued2000-01-01
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent8 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationNkashama, M. N. (2000). Dynamics of logistic equations with non-autonomous bounded coefficients. <i>Electronic Journal of Differential Equations, 2000</i>(02), pp. 1-8.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/9132
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNon-autonomous logistic equation
dc.subjectThreshold-level equation
dc.subjectPositive and bounded solutions
dc.subjectComparison techniques
dc.subjectω-limit points
dc.subjectMiximal and minimal bounded solutions
dc.subjectAlmost-periodic functions
dc.subjectSeparated solutions
dc.titleDynamics of Logistic Equations with Non-autonomous Bounded Coefficients
dc.typeArticle

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