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Considering the mature condition of any individual to have eaten a specific amount of food during the entire period that it can spend at its immature stage, we propose a size-structured model by a first-order quasi-linear partial differential equation. The model can be firstly reduced to a single state-dependent delay differential equation and then to a constant delay differential equation. The state-dependent delay represents intra-specific competition among individuals for limited food resources. A complete analysis of the global dynamics on the positivity and boundedness of solutions, global stability for each equilibrium and Hopf bifurcation is carried out. Our results imply that the delay leads to instability that is shown by a simple example of a certain structured population model. [ABSTRACT FROM AUTHOR]

This work investigates the dynamic behaviors of one-prey multi-predator model with defensive ability of the prey by introducing impulsive biological control strategy. By using the Floquent theorem and the small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, and a permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that the multi-predator impulsive control strategy is more effective than the classical one and makes the behavior dynamics of the system more complex. [ABSTRACT FROM AUTHOR]