Figure 3

Dynamical behaviors of Gd-NPs according to τ for \(f(\tau )=1\) (with \(\tau _{0}=1.96\) and the initial condition \((y_{1}(0), y_{2}(0), y_{3}(0))=(75, 0, 0)\)). (a) When \(\tau =0.30\), a solution of system (1) approaches the Gd-NPs-free equilibrium or Gd-NPs are eventually eliminated from every compartment. (b) When \(\tau =1.70\), a solution oscillates and then eventually tends to the NPs-free equilibrium or the concentration of Gd-NPs fluctuates at a certain period at the beginning of time before Gd-NPs being washed out. (c) When \(\tau =1.96\), a solution oscillates periodically or Gd-NPs periodically circulate in the system. (d) When \(\tau =2.5\), a solution diverges from the Gd-NPs-free equilibrium or Gd-NPs behaviors are unstable