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Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

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  • Josef Diblík
  • Denys Ya. Khusainov
  • Irina V. Grytsay
  • Zdenĕk Šmarda

Abstract

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalue of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

Suggested Citation

  • Josef Diblík & Denys Ya. Khusainov & Irina V. Grytsay & Zdenĕk Šmarda, 2010. "Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-23, June.
    • Handle: RePEc:hin:jnddns:539087
    DOI: 10.1155/2010/539087
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