eng International Academy of Ecology and Environmental Sciences Computational Ecology and Software 2220-721X 2020-12-1 10 4 200 216 4 article Sarker Md. Sohel Rana 1 2 University of Dhaka, Dhaka 1000, Bangladesh We consider a discrete-time predator-prey system with Holling type I functional response and Gompertz growth of prey population to study its dynamic behaviors. We algebraically show that the predator-prey system undergoes a flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB) in the interior of R2+ when one of the model parameter crosses its threshold value. We determine the existence conditions and direction of bifurcations by using the center manifold theorem and bifurcation theorems. We present numerical simulations to illustrate theoretical results which include the bifurcation diagrams, phase portraits, appearing or disappearing closed curves, periodic orbits, and attracting chaotic sets. In order to justify the existence of chaos in the system, maximum Lyapunov exponents (MLEs) and fractal dimension (FD) are computed numerically. Finally, chaotic trajectories have been controlled by applying feedback control method. http://www.iaees.org/publications/journals/ces/articles/2020-10(4)/dynamic-complexity-in-a-discrete-time-predator-prey-system.pdf predator-prey system Gompertz growth bifurcations Lyapunov exponents feedback control