Detecting Dynamic Complexity Of Rat Population In Ecological Systems

There exists intrinsic regularity for each species in nature as a result of multiply and disease. Meanwhile the changing structure of food chain, immigration and emigration of species and environment noises all can make changes to the population of the species, which increases the complexity of species population. The research of dynamic complexity provides rational guidance and methods for the production management and pest control. Presently, the two ways often used in ecological study including statistical analysis of the test sample and simulation models research both can't deal with this situation. The statistical analysis method just can give the general trend based on experience; while to simulation models the effect of the simulation is usually proportional to the complexity of the models. To get the exact result and the inherent character, complicated models have to be constructed which reduces the model's computability and operability.Chaos is the result of continuity and randomness interacting together and reflects the inherent dynamic complexity of the system to some extent. Chaos detecting technologies including Poincare section, correlation dimension analysis and Lyapunov exponent analysis give the complexity of the system separately from different perspectives. And they all build on the basis of statistical data which make them more operable. On the other hand, wavelet methods for time series analysis rising recently can decompose the complexity of the system into different time scales. And the influence of different sampling time interval can be discussed. And the wavelet de-noising technology removes the researching noises caused by inevitable operation error. Then, a real inherent property can be shown by the research. So chaos detecting and wavelet methods widen the research area of complex system and give us more exact result.Based on the actuality of ecological research and the development of analytical technologies used in complex system, main contributions of this dissertation are as follows:1) First two advanced technologies to analyze statistical data are introduced into ecological research: wavelet analysis and chaos detecting technology. This combines the theoretical analysis and actual operation together and enriches the ecological research area. What's more is that the operation is easier to be carried out.2) Multi-resolution chaos analysis technology is proposed. It firstly decomposes the system data into different time scales using the decomposing advantage of the wavelet transform method. Then chaos of data from different scales is detected by a number of chaotic technologies. Multi- resolution chaos detection method can extract the chaos character of the system data in different time scales.3) De-noised chaos detection method is constructed. It makes de-noising process before the chaos detection using wavelet de-noising technology. Through the analysis of the clear data, the influence of noise caused by environment condition's changing and experiment operation error are made clear.4) Base on the theoretical of the above technologies, the dynamic complexities of rat species in some ecological system are researched. The characters are studies from different points of view.5) At last, chaos forecasts of the rat population analyzed above are given. As chaotic data can't be predicted exactly by linear prediction technology and long term prediction, chaos forecast is used to make up this area. And the results prove it very useful.