This thesis is concerned to dynamics of some models in ecology and epidemiology . In fact , we consider a discrete-time prey-predator Ricardo-Malthus model and also a SIS discrete-time epidemic model . For the Ricardo-Malthus model , we investigate , stability of positive fixed point , period-doubling bifurcation , Neimark-Sacker bifurcation , resononce 1:2 bifurcation and resononce 1:3 bifurcation . We introduce normal forms of these bifurcations . Then , we consider SIS epidemic model . We study , stability of equlibria , resononce 1:2 and resonance 1:4 bifurcations and then we compute normal forms of bifurcations . To illustrate our result , we simulate bifurcation diagrams and phase portraits for some parameters . Also , by computing the Lyapunov exponents , we observe the chaotic dynamics in these two models . In recent years, the discrete dynamical models are widely investigated. The reasons are that many the discrete models are more realistic than the continuous models. For example in epidemic models since the epidemic statistics are compiled from given time intervals and not continuously. Such discrete models not only study with good accuracy the behavior of the continuous models, but also assess the effect of larger time steps. It is well known, for the discrete epidemic models, the main research subjects include the computation of the basic reproduction number, the local stability and global stability of the disease-free equilibrium and endemic equilibrium, the extinction, persistence and permanence of the disease, bifurcations and chaos phenomena of models, etc. Many important and interesting research works can be found in the references cited therein. On the other hand, it is well known that the bifurcation theory is a very important tool in the understanding of the dynamical behaviors for a dynamical system. It is based on several techniques that look for the simplification of a given dynamical system, leading to canonical systems whose analysis will provide interesting information for the original system. Usually, in order to reach these simplifications, the method of center manifolds and normal forms are used for the reduced system. We see that in recent years the bifurcation problems for dynamical systems are widely investigated. The dynamics of a discrete-time Ricardo–Malthus model obtained by numerical discretization is investigated, where the step size regarded as a bifurcation parameter. It is shown that the system undergoes flip bifurcation and Neimark–Sacker bifurcation in the interior of $ R^2_+ $ by using the theory of center manifold and normal form. Numerical simulations are presented not only to illustrate our theoretical results, but also to exhibit the system’s complex dynamical behavior, such as the cascade of period-doubling bifurcation periodic orbits and quasiperiodic orbits, and the chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. Then dynamical complexity of a discrete SIS epidemic model with standard incidence by the qualitative analysis and numerical simulations. It is verified that there are the codimension-two bifurcations associated with 1:2 and 1:4 strong resonances and chaos phenomena. The results are established by using the bifurcation theory and the normal form method. Furthermore, the numerical simulations are obtained by the phase portraits, the codimension-two bifurcation diagrams, for two different varying parameters. The results obtained, show that a discrete SIS epidemic model can have very rich dynamical behaviors.