Stability Analysis of a System of Exponential Difference Equations
We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/375890 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-yn-1)/(a2+b2xn+c2xn-1), where the parameters αi, βi, γi, ai, bi, and ci for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results. |
|---|---|
| ISSN: | 1026-0226 1607-887X |