Logistic equation on time scales

We propose a new dynamic logistic equation that, in contrast with the one available in the literature, preserves the non-negativity of its solutions, which is an essential property for biological meaning. We derive the exact solution of the proposed model and analyze its behavior on arbitrary time s...

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Bibliographic Details
Published inExamples and counterexamples Vol. 8; p. 100197
Main Authors Lemos-Silva, Márcia, Torres, Delfim F.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Discrete and quantum logistic growth models
Dynamic consistence
Exact solution
Logistic equation on time scales
Non-negative solutions
Logistic equation on time scales
Dynamic consistence
92D25
34N05
Non-negative solutions
Exact solution
Discrete and quantum logistic growth models
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ISSN2666-657X
2666-657X
DOI10.1016/j.exco.2025.100197

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Summary:We propose a new dynamic logistic equation that, in contrast with the one available in the literature, preserves the non-negativity of its solutions, which is an essential property for biological meaning. We derive the exact solution of the proposed model and analyze its behavior on arbitrary time scales. Finally, we illustrate our results with concrete examples. Our key novelty is: the model’s ability to maintain positivity across general time scales and its dynamic consistency with the classical logistic equation.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2025.100197