Opuscula Math. 38, no. 1 (2018), 95-115
https://doi.org/10.7494/OpMath.2018.38.1.95

 
Opuscula Mathematica

On the stability of some systems of exponential difference equations

N. Psarros
G. Papaschinopoulos
C. J. Schinas

Abstract. In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.

Keywords: difference equations, asymptotic behaviour, global stability, centre manifold, biological dynamics.

Mathematics Subject Classification: 39A10.

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  • N. Psarros
  • Democritus University of Thrace, School of Engineering, Xanthi, 67100, Greece
  • G. Papaschinopoulos
  • Democritus University of Thrace, School of Engineering, Xanthi, 67100, Greece
  • C. J. Schinas
  • Democritus University of Thrace, School of Engineering, Xanthi, 67100, Greece
  • Communicated by Stevo Stević.
  • Received: 2017-03-30.
  • Revised: 2017-04-29.
  • Accepted: 2017-05-01.
  • Published online: 2017-11-13.
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Cite this article as:
N. Psarros, G. Papaschinopoulos, C. J. Schinas, On the stability of some systems of exponential difference equations, Opuscula Math. 38, no. 1 (2018), 95-115, https://doi.org/10.7494/OpMath.2018.38.1.95

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