The trp operon encodes the five genes for the enzymes required to convert chorismate to tryptophan, and its switching on and off is controlled by both feedback repression and attenuation in response to different levels of tryptophan in the cell. Repression of the operon occurs when tryptophan concentration is high, and attenuation fine-tunes the transcription level at a lower cellular concentration of tryptophan. An extended mathematical model is established in this study to describe the switching on and off of the trp operon by considering the integrated effects of repression and attenuation. The influences of cell growth rate on the biosynthesis of tryptophan, stability and dynamic behavior of the trp operon are investigated. Sustained oscillations of tryptophan levels are predicted from the regulated turning on and off of the trp operon. It is interesting to note that during such oscillations the regulation of transcription displays a kind of "on" and "off' state in terms of gene expression, indicating the existence of a genetic circuit or switch in the regulation of the trp operon. Time lags between transcription and translation are also predicted and may explain the occurrence of such oscillation phenomenon.