In this research project, we explore technological backgrounds of mathematical models related to information processing in the brain as well as next-generation AI based on such models, review the possibility of realization of such next-generation AI technology and trends of state-of-the-art research, and propose important tasks necessary for the realization of next-generation AI that learns from the dynamic brain particularly from the viewpoint of nonlinear dynamics with a focus on both functions of the normal brain and dysfunctions of the impaired brain. Then, we develop basic mathematical technology for innovative brain-type algorithms, and consider its applicability to robotics and mental illnesses.