  In this article, we investigate the competing Glauber-type and Kawasaki-type
dynamics with small-world network (SWN) effect, in the framework of the
Gaussian model. The Glauber-type single-spin transition mechanism with
probability p simulates the contact of the system with a heat bath and the
Kawasaki-type dynamics with probability 1-p simulates an external energy flux.
Two different types of SWN effect are studied, one with the total number of
links increased and the other with it conserved. The competition of the
dynamics leads to an interesting self-organization process that can be
characterized by a phase diagram with two identifiable temperatures. By
studying the modification of the phase diagrams, the SWN effect on the two
dynamics is analyzed. For the Glauber-type dynamics, more important is the
altered average coordination number while the Kawasaki-type dynamics is
enhanced by the long range spin interaction and redistribution.
