Qualitative Tools for Studying Periodic Solutions and Bifurcations as Applied to the Periodically Harvested Logistic Equation

DOI10.1080/00029890.2008.11920518zbMath1361.34038OpenAlexW2404617505MaRDI QIDQ3606567

Diego M. Benardete, Benedict J. Pollina, V. W. Noonburg

Publication date: 26 February 2009

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2008.11920518

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Symmetries, invariants of ordinary differential equations (34C14) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (18)

Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model ⋮ Phase portraits of the complex Abel polynomial differential systems ⋮ Dynamics of a single species in a fluctuating environment under periodic yield harvesting ⋮ Separated solutions of logistic equation with nonperiodic harvesting ⋮ Rational solutions of Abel differential equations ⋮ Centers and limit cycles for a family of Abel equations ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ Periodic dynamics of a single species model with seasonal Michaelis-Menten type harvesting. II: Existence of two periodic solutions ⋮ Periodic dynamics of a single species model with seasonal Michaelis-Menten type harvesting ⋮ Existence of at most two limit cycles for some non-autonomous differential equations ⋮ Limit cycles of Abel equations of the first kind ⋮ Harvesting a logistic population in a slowly varying environment ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Stability of singular limit cycles for Abel equations ⋮ Periodic solutions of a logistic type population model with harvesting ⋮ On the rational limit cycles of Abel equations ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions ⋮ Planar systems and Abel equations

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