The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase spac...The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O+ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.展开更多
This paper gives a group of formal definitions of derivation of the qualitativebehavior of a system from the qualitative structural descriptions and the initial state of thesystem.A new qualitative simulation algorith...This paper gives a group of formal definitions of derivation of the qualitativebehavior of a system from the qualitative structural descriptions and the initial state of thesystem.A new qualitative simulation algorithm QSIM is proposed,it can derive thequalitative behavior description efficiently,and predict the unknown critical values ofsome parameters and their corresponding values in a system.The application of QSIM isdemonstrated with an example.展开更多
文摘The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O+ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.
文摘This paper gives a group of formal definitions of derivation of the qualitativebehavior of a system from the qualitative structural descriptions and the initial state of thesystem.A new qualitative simulation algorithm QSIM is proposed,it can derive thequalitative behavior description efficiently,and predict the unknown critical values ofsome parameters and their corresponding values in a system.The application of QSIM isdemonstrated with an example.
