Abstract
The study focuses on the model of houseflies with discrete delay, which is examined both theoretically and numerically. The solution of the delayed system is bounded and positive. The delay is selected as the bifurcation parameter. Stability analysis, local and global Hopf bifurcation are given in theoretical aspect. Through computer simulations, various dynamic behaviors, such as supercritical Hopf bifurcation, are detected. The theoretical analysis and numerical observations in this research are significant contributions to the biomathematics research area.
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