Figure 7

Dynamical behaviors of Gd-NPs according to τ for \(f(\tau )=e^{-k_{31}\tau }\). (a) The concentration of Gd-NPs changes according to time when \(\tau =0.30\). (b) A phase portrait of (1) when \(\tau =0.3\). It shows that a solution approaches the Gd-NPs-free equilibrium (c) The concentration of Gd-NPs changes according to time when \(\tau =2.5\). (d) A phase portrait of (1) when \(\tau =2.5\). Eventually, a solution will approach the Gd-NPs-free equilibrium