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Relaxation Oscillations in a Logistic Equation with State-in-the-Past-Dependent Delay

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An Erratum to this article was published on 23 September 2021

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Abstract

A logistic equation with a delay depending on the state in the past is considered. We study the question of the existence of nonlocal relaxation periodic solutions of this equation for large values of the parameter. The characteristics (for example, period and extreme values) of solutions that we find are compared with similar characteristics of solutions of other modifications of this equation. Asymptotic estimates for the period and the maximum and minimum values are obtained. The study is carried out by the large parameter method.

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References

  1. A. Yu. Kolesov and Yu. S. Kolesov, “Relaxational oscillations in mathematical models of ecology,” Proc. Steklov Inst. Math., 199 (1995).

    Google Scholar 

  2. G. E. Hutchinson, “Circular causal systems in ecology,” Ann. N. Y. Acad. Sci., 50, 221–246 (1948).

    Article  ADS  Google Scholar 

  3. S. A. Kaschenko, “Asymptotics of solutions of the generalized Hutchinson’s equation,” Model. Anal. Inform. Sist., 19, 32–61 (2012).

    Article  Google Scholar 

  4. V. O. Golubenets, “Relaxation oscillations in a logistic equation,” Math. Notes, 107, 890–902 (2020).

    Article  MathSciNet  Google Scholar 

  5. M. C. Mackey, “Commodity price fluctuations: price dependent delays and nonlinearities,” as explanatory factors J. Econom. Theory, 48, 497–509 (1989).

    Article  MathSciNet  Google Scholar 

  6. Yu. S. Kolesov and D. I. Shvitra, “Matematicheskoe modelirovanie protsessa goreniya v kamere zhidkostnogo raketnogo dvigatelya,” Litovskiy matem. sb., 15, 153–167 (1975).

    Google Scholar 

  7. T. Insperger, D. A. W. Barton, and G. Stépán, “Criticality of Hopf bifurcation in state- dependent delay model of turning processes,” Internat. J. Non-Linear Mech., 43, 140–149 (2008).

    Article  ADS  Google Scholar 

  8. M. G. Zager, P. M. Schlosser, and H. T. Tran, “A delayed nonlinear PBPK model for genistein dosimetry in rats,” Bull. Math. Biol., 69, 93–117 (2007).

    Article  MathSciNet  Google Scholar 

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Funding

The reported study was funded by RFBR, project no. 19-31-90082.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, Russia

    V. O. Golubenets

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  1. V. O. Golubenets
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Correspondence to V. O. Golubenets.

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The author declares no conflicts of interest.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 389-402 https://doi.org/10.4213/tmf10042.

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Golubenets, V.O. Relaxation Oscillations in a Logistic Equation with State-in-the-Past-Dependent Delay. Theor Math Phys 207, 738–750 (2021). https://doi.org/10.1134/S0040577921060052

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  • DOI: https://doi.org/10.1134/S0040577921060052

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