Effects of time delays in a mathematical bone model Project supported by the National Natural Science Foundation of China (Grant No. 11474117). |
(color online) Kinetic behaviors of the system without time delays. The time evolution of the number of osteoclasts (a), the number of osteoblasts (b), the tumor (c), the ratio of C(t) to B(t) (e), and the bone mass (f). (d) The numbers of both osteoclasts and osteoblasts in phase plane. |