Dynamic Analysis And Almost Periodic Solution Of Some Biological Models

In this thesis,three biological modelling systems are taken as the object of the research,we thoroughly investigate the global dynamical behavior for ocean rocky in-tertidal community of wild ecosystem(Barnacle-Algae-Mussel system),and the al-most periodic solutions to two biological modelling systems(Hematopoiesis system and Nicholson's blowflies system)with delays,respectively.Firstly,we thoroughly study theoretical analysis for the barnacle-algae-mussel in-teractions model of rocky intertidal community which is introduced by the famous ecol-ogist Huisman and his collaborators,and totally describe the dynamical behavior of the autonomous system.In particular,we prove that global asymptotic stability for the 3-dimensional Mussel-free system,and provide an amenable necessary and sufficient condition for the uniform persistence for the 4-dimensional Mussel-present system.Ac-tually,from the natural observed data supported by Huisman et al,we find that the data is just one special case of our assumptions,and then,the system displayed the dynamical behavior which is consistent with their simulations.As a consequence,for the associated autonomous system,our results rigorously confirm the occurrence of the phenomenon provided by Huisman et al,and some basic priori information are supplied to prove the chaos in this model with external seasonal periodic forcing.Secondly,we focus on almost periodic behavior for almost periodic-forced bio-logical models with delays.On one hand,hematopoiesis model with discrete delays is investigated.We classify these parameters of the model,and overcome the difficulty of the restrictions that the nonlinear terms needed to be monotone and bounded.Some sufficient conditions of the existence for the almost periodic solutions to hematopoiesis differential and difference systems with discrete delays are given.Our obtained results automatically cover the known results with the existence of almost periodic solutions for hematopoiesis models.On the other hand,we investigate the existence of almost periodic solutions for almost periodic-forced Nicholson's blowflies models with neutral type delays,the results are proved that this model can admit almost periodic behavior.Then,these key criteria can guarantee almost periodic behavior of hematopoiesis model and Nicholson's blowflies model are helpful to study oscillation dynamical behavior of these models.