The qualitative analysis for a differential system of the P53-Mdm2 interaction with delay kernel

Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such as transcripion factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. This paper investigates the dynamic P53-Mdm2 interaction model with distributed delays and weak kernel. Choosing the delay or the kernel's coefficient as a bifurcation parameter, we study the direction and stability of the bifurcating periodic solutions. Some numerical examples are finally given in order to justify the theoretical results.