Relaxation Oscillations in a Logistic Equation with Nonconstant Delay

Abstract

A logistic equation with state- and parameter-dependent delay is considered. The existence of a nonlocal relaxation periodic solution of this equation is proved for sufficiently large parameter values. The proof is carried out by using the large parameter method. For large parameter values, asymptotic estimates of the main characteristics of this solution are also constructed.

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Funding

This work was supported by the Russian Foundation for Basic Research under grant 19-31-90082.

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Correspondence to V. O. Golubenets.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 6, pp. 833–847.

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Golubenets, V.O. Relaxation Oscillations in a Logistic Equation with Nonconstant Delay. Math Notes 107, 920–932 (2020). https://doi.org/10.1134/S0001434620050223

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Keywords

  • delay equation
  • relaxation solution
  • large parameter method