A threshold strategy model is proposed to demonstrate the extinction of tumor load and the mobilization of immune cells. Using Filippov system theory, we consider global dynamics and sliding bifurcation analysis. It was found that an effective model of cell targeted therapy captures more complex kinetics and that the kinetic behavior of the Filippov system changes as the threshold is altered, including limit cycle and some of the previously described sliding bifurcations. The analysis showed that abnormal changes in patients' tumor cells could be detected in time by using tumor cell-directed therapy appropriately. Under certain initial conditions, exceeding a certain level of tumor load (depending on the patient) leads to different tumor cell changes, that is, different post-treatment effects. Therefore, the optimal control policy for tumor cell-directed therapy should be individualized by considering individual patient data.

We investigated the phenomenon of pseudo-Hopf bifurcation in a Filippov Hindmarsh-Rose neuronal system with threshold switching, and the existence of crossing limit cycles was proved by constructing the half-return mapping. Through the threshold control, the firing state of the system could be switched, allowing transitions from a non-periodic state to a periodic state, as well as the evolution from spiking to bursting. Furthermore, through threshold switching, the system exhibited the coexistence of multiple attractors, the system could be in multiple stable states, or have multiple stable sets that could attract system trajectories. This meant that neuronal system could exhibits diverse dynamical behaviors than being limited to a single stable state. The phenomenon of period-doubling bifurcation also indicated that the system will eventually enter a chaotic state. By extending the analysis to nonlinear neuronal systems, this study contributes to a deeper understanding of complex dynamics and provides valuable insights for designing state switching in the application of neural dynamics.