Abstract:
We construct three-dimensional dynamical systems with piecewise block-linear discontinuous right-hand side that simulate the simplest molecular oscillators. The phase portrait of each of these systems contains a unique equilibrium point and a cycle lying in the complement of the basin of attraction of this point. There are no other equilibrium points in these phase portraits.
Keywords:circular gene network model, phase portrait of nonlinear dynamical system, equilibrium point, invariant domain, step function, periodic trajectory, nonlocal oscillation.
Fulltext:
PDF file (512 kB)