  A new network data transmission strategy was proposed in Zhang \& Chen [2005]
(arXiv:1405.2404), where the resulting nonlinear system was analyzed and the
effectiveness of the transmission strategy was demonstrated via simulations. In
this paper, we further generalize the results of Zhang \& Chen [2005] in the
following ways: 1) Construct first-return maps of the nonlinear systems
formulated in Zhang \& Chen [2005] and derive several existence conditions of
periodic orbits and study their properties. 2) Formulate the new system as a
hybrid system, which will ease the succeeding analysis. 3) Prove that this type
of hybrid systems is not structurally stable based on phase transition which
can be applied to higher-dimensional cases effortlessly. 4) Simulate a
higher-dimensional model with emphasis on their rich dynamics. 5) Study a class
of continuous-time hybrid systems as the counterparts of the discrete-time
systems discussed above. 6) Propose new controller design methods based on this
network data transmission strategy to improve the performance of each
individual system and the whole network. We hope that this research and the
problems posed here will rouse interests of researchers in such fields as
control, dynamical systems and numerical analysis.
