The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises

The stability of tumor-immune responses to chemotherapy system driven by Gaussian white noises is researched because noises can have an important role in tumor treatment. In this system, there are several steady states. In order to explore the stability of these steady states, the upper Lyapunov exponents of linearized system in these steady states are computed by means of second-order algorithm for stochastic simulation Gaussian white noises. The results show that, one steady state is globally asymptotical stable if and only if the noises are weak, but another steady state is always unstable whether the noise is strong or weak. Moreover, the trajectory of system evolution initiating from anywhere is simulated by same algorithm, which proves preceding conclusions and exhibits the globally asymptotical stable steady state is a sink when noises are weak. In fact, the related conclusions give reference value for the effect of chemotherapy on tumor treatment.