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In this paper, we propose a Star cellular neural network (Star CNN) for associative and dynamic memories. A Star CNN consists of local oscillators and a central system. All oscillators are connected to a central system in the shape of a Star, and communicate with each other through a central system. A Star CNN can store and retrieve given patterns in the form of synchronized chaotic states with appropriate phase relations between the oscillators (associative memories). Furthermore, the output pattern can occasionally travel around the stored patterns, their reverse patterns, and new relevant patterns which are called spurious patterns (dynamic memories).