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In the study of dynamical systems, phase portraits play an important role. However, in almost all related text, I only see some standard examples like prey-predator, pendulum etc. I have a rather unclear thought in my head regarding the role of real/imaginary eigenvalues in the system. What role do they play with respect to the system dynamics ? Are there any physical systems that you know of, which only deal with either real or imaginary eigenvalues ? Or any practical cases where one would "want" to deal with any one of those ?

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# Role of eigenvalues in phase portraits

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