Sequential dynamics of high order polynomial automata networks: an application to the Erlang fixed-point equations

摘要

We present results concerning the sequential evolution of p-order polynomial, symmetric automata networks with monotone transition functions. In particular, any such network has a Lyapunov functional, that may, depending on the transition function of the network, be strictly Lyapunov, resulting in all limit cycles of its dynamical evolution in the sequential mode being fixed points. As an application, we use our results to show that it is always possible to solve, via sequential iteration, the Erlang fixed-point equations, an important fixed point problem which appears in the theory of teletraffic networks.