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We study the forward self-similar solutions to a parabolic system modeling chemotaxisin the whole space R 2 ; where t is a positive constant. Using the Liouville-type result and the method of moving planes, it is proved that self-similar solutions ðu; vÞ must be radially symmetric about the origin. Then the structure of the set of selfsimilar solutions is investigated. As a consequence, it is shown that there exists a threshold in R

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