| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 97 === Transitions in ecological systems often occur without apparent warning. Thus an effective way of prediction is in strong demand. Recent researchers proposed that decreasing ecological resilience can signal an upcoming transition. Unfortunately, it is very difficult to measure the resilience in practice. Therefore, we need some indicator to measure it. Some recent works in the literatures investigated that critical slowing down is a good indicator of ecological resilience. In this report, we use analytical and numerical methods to characterize several results about two-species generalized predator-prey model, three species food chain model, and generic control system. These results can lead directly to predict more complex systems in ecology or real world.
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