The Study Of The Marine Ecosystem Cycling Model Based On Control Theory

Modern Control Theory and Laplace transform are applied to establish the cycle model of the marine ecosystem, and to analyze the phenomena of marine ecosystems. The numerical solution of mode 1 and its stability were studied.Linear algebra and differential equations are the main mathematical tools of Modern Control Theory which analyses, designs and controls system based on state space method. The state space method essentially is a time domain method, which not only describes the external characteristics and the internal state of a system but also show the performance of the system. Research object of Modern Control Theory can be a multivariable, nonlinear, time-varying and discrete system. Research object of marine ecosystem dynamics is ecological system whose manifestation is differential equations. The various phenomena and processes of marine ecosystems are a kind of universal life system, and also are the results of many factors which interact, affect and restrict with each other, the entire system is a multivariable, time-varying and nonlinear circulatory system, and should be classified into application areas of Modern Control Theory.In the first part of the thesis, the author discusses the study status of marine ecosystem model, summarizes and analyzes the various models, evaluates their advantages and disadvantages, and finds out some points need to be improved. The author finds that although there are lots of models, they have not taking into account the biological "cycle" feature.In the second part of the thesis, the author firstly creates a class control system model of marine ecosystems (zero-dimensional three-variable model of Nutrient-Phytoplankton- Zooplankton), and then adopts appropriate empirical formula as a mathematical expression of charged object. Secondly, the author analyzes the equation with the stability theory, makes linearization reasonably practicable, and identifies the parameter space which makes the mode 1 stable with the Lienard-Chipard criterion. Thirdly, state space analysis of Modern Control Theory is applied. Transfer function of the circulatory system can be obtained via Laplace transform on the equation. Finally, the root locus method is applied to analyze the transfer function in order to get a stable condition of marine ecosystems, and analyze the various phenomena of ecological systems.In the third part of the thesis, the author proposes another numerical solution to the nonlinear model. Firstly, the equivalent mode 1 is transformed via Laplace transform. Secondly, S product theory is applied to the product of Laplace transform, and the original equation is simplified to the algebraic equation. Thirdly, numerical solutions are obtained, and then their physical meaning is analyzed. Finally, Matlab's graphical user interface is applied to package this method, making it a marine ecosystem model of the adjustable parameter solution software.This thesis addresses the following issues:Firstly, because most of the differential equations are unable to obtain analytical solutions, related properties of marine ecosystem mode 1 which they represent for cannot be analyzed. From the analysis of the stability and numerical solution of a closed interval, the author comprehensively analyzes related properties of the model. Secondly, when the author analyzes the stability of the mode 1, Modern Control Theory and root locus analysis method are applied to simplify the process of parameter estimation, and stability of the mode 1 can be judged from the root locus chart. Thirdly, under the situation that analytical solution of the equation cannot be obtained, S product theory of Laplace transform is applied to greatly simplify the process of solving the numerical solution in any finite closed interval with high precious. Finally, according to the process of solving the numerical solution, Matlab's graphical user interface, is applied to package this method, making it a marine ecosystem model of the adjustable parameter solution software. And then numerical solution of this method is compared with the Matlab built-in method of solving differential equation solution.