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*Chlorella*is an important species of microorganism, which includes about 10 species.

*Chlorella*USTB01 is a strain of microalga which is isolated from Qinghe River in Beijing and has strong ability in the utilization of organic compounds and was identified as

*Chlorella*sp. (H. Yan etal, Isolation and heterotrophic culture of

*Chlorella*sp.,

*J. Univ. Sci. Tech. Beijing*, 2005,

**27**:408-412). In this paper, based on the standard Chemostat models and the experimental data on the heterotrophic culture of

*Chlorella*USTB01, a dynamic model governed by differential equations with three variables (

*Chlorella*, carbon source and nitrogen source) is proposed. For the model, there always exists a boundary equilibrium, i.e.

*Chlorella*-free equilibrium. Furthermore, under additional conditions, the model also has the positive equilibria, i.e., the equilibira for which

*Chlorella*, carbon source and nitrogen source are coexistent. Then, local and global asymptotic stability of the equilibria of the model have been discussed. Finally, the parameters in the model are determined according to the experimental data, and numerical simulations are given. The numerical simulations show that the trajectories of the model fit the trends of the experimental data well.

Furthermore, we also present a review of the SIR, SEIR epidemic models, with and without delays, appeared in literature, that can be seen as particular cases of the approach presented in the paper.

In this paper, we propose a latent HIV infection model with general incidence function and multiple delays. We derive the positivity and boundedness of solutions, as well as the existence and local stability of the infection-free and infected equilibria. By constructing Lyapunov functionals, we establish the global stability of the equilibria based on the basic reproduction number. We further study the global dynamics of this model with Holling type-Ⅱ incidence function through numerical simulations. Our results improve and generalize some existing ones. The results show that the prolonged time delay period of the maturation of the newly produced viruses may lead to the elimination of the viruses.

One of the important ecological challenges is to capture the complex dynamics and understand the underlying regulating ecological factors. Allee effect is one of the important factors in ecology and taking it into account can cause significant changes to the system dynamics. In this work we consider a two prey-one predator model where the growth of both the prey population is subjected to Allee effect, and the predator is generalist as it survives on both the prey populations. We analyze the role of Allee effect on the dynamics of the system, knowing the dynamics of the model without Allee effect. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee effect enriches the local as well as the global dynamics of the system. Specially after a certain threshold value of the Allee effect, it has a very significant effect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurcations such as the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.

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