Abstract
We construct an invariant two-dimensional surface in the phase portrait of a certain six-dimensional dynamical system considered as a model for the circular gene network functioning. This invariant surface contains an equilibrium point $$S_0 $$ of the system, and if $$S_0 $$ is hyperbolic then this surface contains a cycle of the system. The conditions for the existence of a cycle of this and similar systems were obtained earlier.
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