Stability Analysis And Controller Design Of The Ecological Model Based On Sum-of-Squares Method

There are many complex structure in biological dynamics systems. For instance, Bifurcation, stability, the equilibrium point, controller, the domain of attraction and so on are worth to search. Combining the sum-of-squares and biological dynamics systems model, this thesis has not only used sum-of-squares to analysis stability and domain of attraction of the model but also based on the model to increase the accuracy of computation using sum-of-squares. And it has compared the computational results basing on the sum-of-squares and lagrange multiplier method.About the two-dimension model with stage-structure, this thesis has given the condition to satisfy the equilibrium point existing and has proven it. When designing the controller of the model, sum-of-squares calculation has verified that the change from the Jacobi matrix determinant is less than zero to the Jacobi matrix determinant is more than zero. When using sum-of-squares to judge whether the origin of the system is semi-global exponential stability, if the selected deg of the Lyapunov function has increased, the solution of the index value will be moved away from the origin, Contrasting the sum-of-squares method and lagrange multiplier method, this thesis has gotten the result that basing on sum-of-squares was better than basing on lagrange multiplier method.About the three-dimension model with different food-chains, this thesis has discussed the positive equilibrium. Like the two-dimension model, has given to and proven the condition of the stability of positive equilibrium point, discussed the controller and the domain of attraction, and gotten another condition to increase the accuracy of computation using sum-of-squares.