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We consider a system of equations with discontinuous right hand
side, which arise as models of gene and neural networks. We study
attractors in $R^4$ which lie in a set of orthants in the form of
figure eight. We find that if the attractor is symmetric with
respect to these two loops, then the only possible attractor is a
periodic orbit which traverses both loops once. We show that
without the symmetry the set of admissible attractors include
periodic orbits which follow one loop $k$ times and other loop
once, for any $k$. However, we also show that no trajectory in an
attractor can traverse both loops more then once in a row.