Stability Analysis Of Switched Circulant Systems In Hypercycles

In this paper, we address the stability problem of the hypercycle systems. For switched nonlinear circulant systems using the linear circulant systems and the common Lyapunov function, we give a necessary and sufficient condition on asyptotically stability. For the two nonlinear circulant systems, we describe their competition mechanisms and dynamics by the computer simulation.The constructing of mathematical models of biological evolution is an important theme of systems biology, the hypercycles describe the self-replication systems of biological macromolecules. A number of stability criteria for the switched linear circulant systems based on the common Lyapunov function and LMI are presented, as well as a necessary and sufficient condition for the switched nonlinear system. At last, we give some theoretical descriptions of biological experiments for the two nonlinear competitive systems by the computer simulation.