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In this paper, we investigate a type of Pielou's difference system withexponential term  $$  y_{n+1}=\frac{az_n}{p+z_{n}}e^{-y_n},\; \;\;\;\;\;  z_{n+1}=\frac{by_n}{q+y_{n}}e^{-z_n}.  $$ where the parameters $a,b,p,q, $ are positive real numbers and the initialvalues $y_0,z_0$ are arbitrary nonnegative real numbers. Using the mean valuetheorem and Lyapunov functional skills, we obtained some sufficient conditionswhich guarantee the boundedness and persistence of the solution, and globalasymptotic stability of the equilibriums. Moreover, two numerical examples aregiven to elaborate on the results.

Dynamical behavior of Pielou's difference system with exponential term