Dynamic Analysis of a Logarithmic Population Model with Piecewise Constant Arguments.

In this paper, we consider a logarithmic population model with piecewise constant arguments. First, we study the uniqueness and existence range of the equilibrium point of the model. After that, by using the linearized stability theorem, the semicycle property and a suitable Lyapunov function, some sufficient conditions are obtained for the local and global asymptotic stability of the equilibrium point and the damped oscillation of positive solutions of the model. Finally, some examples with computer simulations are given to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]