Analysis And Control Of Biology System With Invasion Of Alien Species

The biomathematics is trying to study and solve the biological problem from the angle of mathematics through mathematical thinking.The invasion of exotic species often damages the local ecological system and geographical structure,which has a negative impact on production and life.Using mathematical biology to study the ecological system with alien species invasion and realize economic production and population dynamics behavior,which plays a positive role in the stability and development of human society.Based on the background of the invasion of alien species,the thesis introduced the ecological systems of three different kinds of biological relationship,including predation,inhibition and competition,and the three ecological systems in this thesis were considering the population with stage structure.First of all,according to the existing predator-prey relation of alien species and the species of original ecological system,the analysis of permanent functional of ecosystem with stage structure and functional response function was showen.Then,according to the singular biological economic theory and considering that the invasive species released chemicals which affected the local species and the local species had delay change,the thesis analyzed the Hopf bifurcation,equilibrium point and cycle of the delayed biological model with stage structure.Thirdly,considering that the exotic species and the local species competed,the H?guaranteed performance control was analyzed on a biological economy system with a certain disturbance.The specific research work was as follows:(1)The background of this thesis was introduced,in which the thesis introduced the nowadays invasion situation of alien species,its cause and its effect,emphatically analyzed the fish population survival and fishing under the invasion of alien species,and then introduced the analysis method of biological control,including the analysis of the Holling IV system with stage structure,Hopf bifurcation analysis of time-delay systems the biological system and guaranteed performance control analysis.Besides,the thesis introduced the research progress of alien species and the generalized biological system.In the end,the chapter expounded the main contents of this study.(2)The thesis focused on a non-autonomous predator-prey system with Holling IV and stage structure under the predator-prey relationship.Based on the two kindsgrowth models,a biological predation model of this thesis was obtained.Then through the analysis and verification,a set of sufficient conditions for the permanent existence of the system was obtained,which means if the conditions were satisfied,a long-term coexistence state could be achieved among all the species involved in the ecosystem,and the illustration was given by a set of simulation examples.(3)Biological economy system with a delay and stage structure was studied under the inhibition relationship.The thesis used proper parametric and linear transformation method and applied the method of the center manifold theory and Poincare normalized form to analyze the direction and stability of Hopf bifurcation and its periodic orbit.The correctness of the conclusion is verified through a set of simulation examples shown.(4)The problem of guaranteed cost control of a singular biological economic system with stage structure under the competition relation was concerned in this chapter.Considering the artificial capture and the purification ability of alien species,a generalized system model was developed.The properties of equilibrium points around were discussed.Besides,through the T-S fuzzy method,generalized linear biology model was developed.On the basis of it,considering that the disturbance affected by some natural factors satisfied Lipschitz conditions,the thesis determined the performance index.Using LMI method,a set of sufficient conditions on the existence of guaranteed controller was given which satisfy guaranteed performance index.A set of numerical simulation was shown to verify the effectiveness of the study result.