S. A. Kaschenko and D. O. Loginov, “About Global Stable of Solutions of Logistic Equation with Delay”, IOP Journal of Physics: Conf. Series 937, 012019 (2017).

S. A. Kaschenko and D. O. Loginov, “About Global Stable of Solutions of Logistic Equation with Delay”, IOP Journal of Physics: Conf. Series 937, 012019 (2017).

ABSTRACT 

The article is devoted to the definition of all the arguments for which all positive solutions of logistic equation with delay tend to zero for t → . The authors have proved the acquainted Wright's conjecture on evaluation of a multitude of such arguments. An approach that enables subsequent refinement of this evaluation has been developed.

References

[1] Wright E M 1955 A non-linear difference-differential equation Journal für die reine und angewandte Mathematik (Crelles Journal) 194 66-87

[2] Kuang Y 1993 Mathematics in Science and Engineering 191 (New York: Academic Press) Delay differential equations with applications in population dynamics

[3] Gourley S A, So J and Wu J 2004 Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics J. Math. Sci. 124 5119-5153 Crossref

[4] Kakutani S and Markus L 1958 On the non-linear difference differential equation y′(t) = [A + By(t − γ)]y(t) 4 (Princeton: Contributions Theory Nonlinear Oscillation) 411-418

[5]Grigorieva E V and Kashchenko S A 1993 Regular and chaotic pulsations in laser diode with delayed feedback Int. J. Bifur.& Chaos 3 1515-1528 Crossref

[6] Kashchenko S A 1985 K voprosu ob otsenke v prostranstve parametrov oblasti globalnoy ustoychivosti uravneniya Hatchinsona (in Russian) [On the problem of estimating in the parameter space the domain of global stability of the Hutchinson equation] (Yaroslavl: Nelineynye kolebaniya v zadachakh ekologii YarGU) 55-62

[7] Kashchenko S A 2012 Asimptotika resheniy obobcshennogo urovneniya Hatchinsona (in Russian) [Asymptotics of the Solutions of the Generalized Hutchinson Equation] 19 (Yaroslavl: Modelirovanie i analiz informacionnih sistem) 32-61

[8] Kashchenko S A 2013 Asymptotics of the Solutions of the Generalized Hutchinson Equation Automatic Control and Computer Sciences 47 470-494 Crossref

[9] Bánhelyi B, Csendes T, Krisztin T and Neumaier A 2014 Global attractivity of the zero solution for Wright’s equation SIAM Journal on Applied Dynamical Systems 13 537-563 Crossref