Existence And Global Attactivity Of Positive Periodic Solutions For Two Kinds Of Lotka-volterra Systems With Deviating Arguments

In 1926, Italian mathematician V. Volterra published the famous paper to explain the regularity for variation of fish in the harbor Finme which D'Ancona proposed and put forward the celebrated Lotka-Volterra model (A. J. Lotka also brought forward this model through the research of chemistry experiment in 1925), and since then the theory of dynamical systems had been extensively applied to biology. In the beginning, the model A.J. Lotka and V. Volterra presented is a kind of predator-prey systems, and consequently such as competitive type models and mutual type models were proposed, to which had been gradually paid high at-tention by ecologists.Due to the rationality of functional differential equations, in this thesis, we shall consider the existence and global attractivity of pos-itive periodic solutions for two kinds of Lotka-Volterra systems with deviating arguments. At first Chapter 1 introduces the histories of Lotka-Volterra systems, and then it presents main results, organization and preliminaries of this thesis. In Chapter 2, by using Krasnoselskii's fixed point theorem and constructing Lyapunov functions, we investi-gate the problem of the existence and global attractivity of positive pe-riodic solutions for predator-prey Lotka-Volterra systems with deviating arguments. Chapter 3 obtains some sufficient conditions for the exis-tence and global attractivity of positive periodic solutions for competitor-competitor-mutualist Lotka-Volterra systems with deviating arguments.In this thesis, we deal with two kinds of non-competitive Lotka-Volterra systems, our work improves the previous results, and the meth-ods and hypothesis are very technical and creative. In addition, some results in this thesis have been published in Nonlinear Analysis:Real World Applications and Mathematical and Computer Modelling etc.