Traffic dynamics of regular networks are of importance in theory and practice. In this paper, we study such a problem with a regular lattice structure. We specify the network structure and traffic protocols so that all the random features are removed. When a node is attacked and then removed, the traffic redistributes, causing complicated dynamical results. With different system redundancy, we observe rich dynamics, ranging from stable state to periodic to chaotic oscillation. Since this is a completely deterministic system, we can conclude that the nonlinear dynamics is purely due to the interior nonlinear feature of the traffic.