Sentiment analysis is one of the key tasks of natural language understanding. Sentiment Evolution models the dynamics of sentiment orientation over time. It can help people have a more profound and deep understanding of opinion and sentiment implied in user generated content. Existing work mainly focuses on sentiment classification, while the analysis of how the sentiment orientation of a topic has been influenced by other topics or the dynamic interaction of topics from the aspect of sentiment has been ignored. In this paper, we propose to construct a Gaussian Process Dynamic Bayesian Network to model the dynamics and interactions of the sentiment of topics on social media such as Twitter. We use Dynamic Bayesian Networks to model time series of the sentiment of related topics and learn relationships between them. The network model itself applies Gaussian Process Regression to model the sentiment at a given time point based on related topics at previous time. We conducted experiments on a real world dataset that was crawled from Twitter with 9.72 million tweets. The experiment demonstrates a case study of analysing the sentiment dynamics of topics related to the event Brexit. INDEX TERMS Sentiment analysis, sentiment evolution, dynamic Bayesian network, social media, temporal dynamics.