Fractal Analysis And Prediction Of Several Marine Environments And Algaes

Fractal phenomena exist everywhere in nature,which has beea widely used in mathematics,chemistry,physics,biology,geology,economics and other fields.Julia set and Mandelbrot set that are generated by complex systems are two classic fractal sets in fractal theory,and they are widely studied in control theory,image process-ing,topology analysis,characteristic analysis,perturbation analysis.In this paper,fractal characteristics and control problems of a class of real systems are studied the-oretically,then we apply the theoretical achievements to the growth control of algae cells,achieving the effective growth control,and fractal theory is used to forecast and analysis the global warming.The major contents are as follows:1.Fractal features and synchronization of a class of generalized Logistic mapJulia and Mandelbrot sets of a class of generalized real Logistic map are dis-cussed.The fractal dimension of Julia set of the real map is obtained by box-counting method.When fixed points of the system can be obtained,the control of Julia sets of the system is accomplished via using the linear feedback control.According to the complexity of nonlinear system,if fixed points of the system are difficult to be calcu-lated,the zoom control method can be used to achieve control objectives.Based on the concept of synchronization of Julia sets between different systems,the nonlinear coupling control and gradient control are taken to realizing the synchronization of Julia and Mandelbrot sets of two different systems with different parameters respec-tively.2.Fractal characteristics of Heterocapsa circularisquama and Prorocentrum dentatum cells growthHeterocapsa circularisquama and Prorocentrum dentatum cells growth model is introduced,due to the discussion of fractal properties of M-J sets of the generalized Logistic real map.The set of initial cell densities of H.circularisquama and P.denta-turn and the set of environmental factors disturbing the growth of H.circularisquama and P.dentatum cells are constructed.The result of making H.circularisquama and P.dentatum cells grow according to a given growth target is reached via optimal control and a proper mathematical transform respectively.In addition,approximate or same behaviors of two different sets of initial cell densities of H.circularisquama and P.dentatum and two different sets of environmental factors disturbing the growth of H.circularisquama and P.dentatum cells are realized by introducing the coupling terms respectively.3.Fractal prediction and analysis of global warming The melting process of arctic glacier with the change of temperature parameter is depicted using the filled Julia sets of space complex dynamical system.Furthermore,the filled Julia sets of plane complex dynamical system are used to describe the change of island and ice layer area with the change of temperature parameter.Finally,the fractal dimension of island and ice layer are calculated using the box-counting method,and the rela-tionship between the area of island and ice layer,fractal dimension and temperature parameter are obtained so as to make predictions for sea level rise leading to the decrease of land area.