In order to study the dissemination mechanism of knowledge, a SIRI dynamics model with the learning rate, the forgetting rate and the recalling rate is constructed in this paper. Stability of equilibria and global dynamics of the SIRI model are analyzed. Two thresholds that determine whether knowledge is disseminated are given. We describe the stability of the equilibria for the SIRI model in which there are an equilibrium and a line of equilibria. In particular, we find the dividing curve function which is used to partition invariant set in order to discuss the local stability, and obtain the equation of the wave peak value or wave trough value in the process of knowledge dissemination. Numerical simulations are provided to support the theoretical results. The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters, which play an important role on controlling and administering the knowledge dissemination.

中文翻译：

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具有召回率的SIRI知识传播模型的全局分析

为了研究知识的传播机理，建立了具有学习率，遗忘率和召回率的SIRI动力学模型。分析了SIRI模型的平衡稳定性和整体动力学。给出了两个确定知识是否传播的阈值。我们描述了SIRI模型平衡的稳定性，其中存在一个平衡和一条平衡线。特别地，我们找到了分割曲线函数，该函数用于划分不变集以讨论局部稳定性，并在知识传播过程中获得波峰或波谷值的方程。提供数值模拟以支持理论结果。