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A Delay-Averaged Logistic Model

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Abstract

For the equation x(t) = εx(t) (1-(1/τ) ∫ t-θ-τ t-θ x(u)du), ε > 0, θ > 0, τ > 0, conditions for the stability of a nonzero stationary solution under small perturbations are determined.

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REFERENCES

  1. Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population dynamics, London: Kluwer Academic, 1992.

    Google Scholar 

  2. Cushing, J.M., Integro-Differential Equations and Delay Models in Population Dynamics, Berlin: Springer-Verlag, 1977.

    Google Scholar 

  3. Kolosov, G.E., Control for the Size of a Population Described by a Stochastic Logical Model, Avtom. Telemekh., 1997, no. 4, pp. 192-203.

    Google Scholar 

  4. Volkov, I.K., Krishchenko, A.P., and Chebotarev, A.N., Modes of Population Dynamics with Size Conservation, Avtom. Telemekh., 1997, no. 8, pp. 156-167.

    Google Scholar 

  5. Miller, R.K., On the Volterra Population Equation, SIAM J. Appl. Math., 1966, vol. 14, pp. 446-452.

    Google Scholar 

  6. Gopalsamy, K., Leung, Issic K.C., and Pingzhou Liu., Global Hopf-Bifurcation in a Neural Netlet, Appl. Math. Comput., 1998., no. 94., pp. 171-192.

    Google Scholar 

  7. El'sgol'ts, L.E., Vvedenie v teoriyu differentsial'nykh uravnenii s otklonyayushimsya argumenton (Introduction to the Theory of Differential Equations with a Deviating Argument), Moscow: Nauka, 1964.

    Google Scholar 

  8. Myshkis, A.D., Lineinye differentsial'nye uravneniya s zapazdyvayushim argumenton (Linear Differential Equations with a Delay Argument), Moscow: Nauka, 1972.

    Google Scholar 

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Vagina, M.Y. A Delay-Averaged Logistic Model. Automation and Remote Control 64, 666–671 (2003). https://doi.org/10.1023/A:1023254801276

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  • DOI: https://doi.org/10.1023/A:1023254801276

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