Behavior of a discrete ecological model. (English) Zbl 1521.39009
Summary: We study the persistence, boundedness and unboundedness, existence and uniqueness of positive equilibrium point, local and global asymptotic stability, and rate of convergence of the following system of exponential form difference equations:
\[
x_{n+1}=\alpha_1+\beta_1y_n+\gamma_1y_{n-1}e^{-x_n},\, y_{n+1}=\alpha_2+\beta_2x_n+\gamma_2x_{n-1}e^{-y_n}\,n=0,1,\cdots,
\]
where initial values \(x_{-1}\), \(y_{-1}\), \(x_0\), \(y_0\) and parameters \(\alpha_1,\beta_1,\gamma_1,\alpha_2,\beta_2,\gamma_2\) are positive real numbers. Finally, some numerical examples are given to verify our theoretical results.
MSC:
| 39A22 | Growth, boundedness, comparison of solutions to difference equations |
| 39A30 | Stability theory for difference equations |
| 92D40 | Ecology |
Keywords:
difference equations; boundedness; unboundedness; persistence; local and global asymptotic stability; rate of convergenceReferences:
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