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The dynamic of amoebas in favorable circumstances is modeled by a nonlinear system of Partial Differential Equations arising in chemotaxis. The competition between different parameters of this system plays a major role in the process of aggregation. Throughout this paper, we prove the existence of self-similar solutions that blow up in finite time in a dimensional space and under specific circumstances depending upon the position of those parameters.doi:10.2478/auom-2013-0006 fatcat:yhoceg4sdrbbpopjr672qhiu7a