In this talk, we propose a new mechanism for generating oscillatory fronts in a system of two 
reaction-diffusion (R-D) equations. The equations describe a network of two proteins A and B 
that interact through regulating each other's rate of synthesis by acting on the their respective 
controlling genes. Both proteins exert positive influence on their own rate of synthesis and 
degrade through a first order reaction. Protein A promotes the synthesis of B while B inhibits 
the synthesis of A. In this network, coexistence between two or more stable spatially uniform 
states often occurs. If the diffusion of B is much faster than that of A, spatially non-uniform 
fronts often arise and coexist with the stable uniform states through a mechanism that is 
different from Turing's. The location of the front is dependent on the average level of B, the 
length of the space, and some key parameters. The front can be destabilized giving rise to 
either traveling or oscillatory fronts. The latter resembles the breathing or tango waves observed 
in some other R-D systems. By reducing the system into a shadow system and assuming an abrupt 
"on-and-off" switch for the genes, we are able to solve all the stationary solutions that are monotone 
in space and study their stability. Extension of this analysis to the existence and stability of 
non-montone, multi-peak stationary and oscillatory solutions will also be discussed.  
(This talked is based on a work co-authored with Dr. Heather Hardway.)