Fractal Control In Two Sorts Of Nonlinear Systems

The complex nonequilibrium nonlinear phenomenon widely existed in the u-niverse can be described by a simple method with resort to fractal,which has been found broad applications in the fields such as condensed matter physics,biology,ma-terials science,control theory,chemistry,medicine,seismology,economics,etc..It's of great theoretical research significance and practical application value to study fractalPopulation of an ecosystem is the most important issue in the field of biomath-ematics.Investigation on the population of population paves the way of rational utilization and specifical conservation of wildlife and pest control.The thesis estab-lishes the three-species predator-prey model through theory of Julia set and analyses its stability and synchronization.Thermal diffusion is also seen everywhere in all walks of life related to the nations security and the peoples life,playing a key role in daily production and life.Investigation on thermal diffusion contributes to the thoroush comprehension of its mechanism and guidance and directions in practical life.Previous research mainly on the ground of experiment and statistics,cannot ex-plain the physical nature or represent the thermal diffusion process.To address the problem,the paper establishes the fractal growth model of thermal diffusion within a cylinder wall,and analyses the effect of environmental interference term on the thermal diffusion process to obtain the thermal diffusion control method in specific zone.Details are as follows:1.Fractal feature and control of three-species predator-prey modelThree dimensional and high-dimensional population competition relationship is not rare in nature.Considering that three dimensional prey-competition population can simplify the high-dimensional population competition without loss of generality,to deal with the population evolution,the paper firstly establishes the three-species predator-prey mode by theory of Julia set,and then adopts feedback control to cope with the instability of the system,and finally synchronises the present Julia set with the objective through introduction of coupling control term to optimize system per-formance.The effectiveness of the proposed method has been tested and verified by MATLAB simulation.2.Fractal feature and control of thermal diffusion within cylinder wallControl of thermal diffusion within cylinder wall is a problem requires solving urgently during production and life.To deal with the problem,the paper establishes the fractal growth model of thermal diffusion within a cylinder wall,and analyses the mathematical mechanism of the thermal diffusion process,and accomplishes the thermal diffusion control method in specific zone by change of the environmental interference term.The effectiveness of the proposed method has been tested and verified by MATLAB simulation,too.