Abstract: The present thesis consists of three parts.In the first part, the developing history of the bound ness and global asymptotic characteristic of non-linear system, then the developing history of the theoretical ecology and the discussed problems of the present thesis are introduced.In the first section of the second part, a kind of non-linear system is studied; a sufficient and necessary condition for the bound ness is obtained.In the second section, two kinds of nonlinear systems are studied; four group conditions are established for the nonexistence of periodic solutions. An example is examined by means of these theorems.In the first section of the part three, the criteria for globally stable equilibrium in n-dimensional predator-prey model are obtained.In the second section, the sufficient conditions of the global asymptotic stability and uniqueness of periodic solutions are obtained for n-dimensional model.In the third section, the thresholds for survival and extinction, persistence and extinction of two pieces in a polluted environment are obtained by means of integral mean value…

Key words: Liénard equation; bound ness; periodic solution; Holling’s type Ⅱ functional response; global asymptotic stability; threshold for survival and extinction; extinction; weak persistenc

# Study on Several Inssues of Differential Equations and Biomathematics

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