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Psarros, N.; Papaschinopoulos, G.; Schinas, C. J.

Semistability of two systems of difference equations using centre manifold theory. (English) Zbl 1364.39017

Math. Methods Appl. Sci. 39, No. 18, 5216-5222 (2016).
Authors’ abstract: We study the stability of the zero equilibria of the following systems of difference equations: \[ x_{n+1}=ax_n+by_ne^{-x_n},\quad y_{n+1}=cy_n+dx_ne^{-y_n} \] and \[ x_{n+1}=ay_n+bx_ne^{-y_n},\quad y_{n+1}=cx_n+dy_ne^{-x_n} \] where \(a, b, c\) and \(d\) are positive constants and the initial conditions \(x_0\) and \(y_0\) are positive numbers. We study the stability of those systems in the special case when one of the eigenvalues has absolute value equal to \(1\) and the other eigenvalue has absolute value less than \(1\), using the centre manifold theory.
Reviewer: Miloš Čanak (Beograd)

Cited in 12 Documents

MSC:

39A30 Stability theory for difference equations
39A10 Additive difference equations

Keywords:

semistability; centre manifold; systems of difference equations
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References:

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