On non-uniqueness of cycles in 3D models of circular gene networks

We describe 3-dimensional dynamical systems with piecewise linear right hand sides which simulate functioning of simplest molecualr repressilators and contain infinite one-parametric families of cycles in their phase portraits. An analogous dynamical system with step functions in its right hand sides is constructed; its phase portrait contains two piecewise linear cycles. A surface separating these two cycles is described.