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Online Topic indicates the diffusing process of various attitudes and emotions towards some events expressing and propagating over the Internet. It is an essential for monitoring all online information and ensuring internet information safety to search for the predicting approach of the trend of online topic. Previous methods focus on special social network and lack of versatility because of intensely relying on manual experience, that we are devoted to conquering these shortages. In the manuscript, we divide online topic into unimodal topic and multimodal topic, and multimodal topic is the combination of a series of unimodal topics. We present a generally nonlinear dynamic model to give a description of unimodal online topic diffusion mechanism on heterogeneous social network. The model can capture the long-term development tendency of unimodal topic, So, we present a long-term tendency prediction method of unimodal online topic with help of the dynamic model.But the model is not for multimodal online topic in that their long-term development tendency is made up of a series of unimodal topics’ long-term development tendency, which leads to the unpredictability of their long-term future directions, we propose a short-term population prediction method of unimodal and multimodal online topic diffusion on heterogeneous social network based on the essential relationship between unimodal and multimodal topic. Experimental results are our two methods have good performance on predicting the long-term development tendency of unimodal topic and all topic’s short-term population.

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