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Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems

Author

Listed:
  • Carlo Bianca
  • Massimiliano Ferrara
  • Luca Guerrini

Abstract

This paper deals with the derivation and the mathematical analysis of an autonomous and nonlinear ordinary differential-based framework. Specifically, the mathematical framework consists of a system of two ordinary differential equations: a logistic equation with a time lag and an equation for the carrying capacity that is assumed here to be time dependent. The qualitative analysis refers to the stability analysis of the coexistence equilibrium and to the derivation of sufficient conditions for the existence of Hopf bifurcations. The results are of great interest in living systems, including biological and economic systems.

Suggested Citation

  • Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
    • Handle: RePEc:hin:jnlaaa:736058
    DOI: 10.1155/2013/736058
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    Cited by:

    1. Carlo Bianca & Luca Guerrini & Annie Lemarchand, 2014. "Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Zizhen Zhang & Dianjie Bi, 2016. "Dynamical Analysis of a Computer Virus Propagation Model with Delay and Infectivity in Latent Period," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    3. Zizhen Zhang & Limin Song, 2017. "Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    4. Beibei Wang & Min Zhao & Chuanjun Dai & Hengguo Yu & Nan Wang & Pengfei Wang, 2016. "Dynamics Analysis of a Nutrient‐Plankton Model with a Time Delay," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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