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Designed for researchers and graduate students working on systems with a small parameter, this book helps readers get up to date on the knowledge required to start research in this area. It provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. The text contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations, including recently developed approaches based on the direct Lyapunov method and the comparison technique.