Figure 3

Numerical simulation of equations (4a)-(4d). The solution trajectory approaches a limit cycle as time passes. Here, all parameters are chosen to satisfy the conditions in Theorem 3, \({a_{1}}=0.75\), \({a_{2}}=0.3\), \({a_{3}}=0.35\), \({a_{4}}=0.9\), \({a_{5}}=0.4\), \({b_{1}}=0.7\), \({b_{2}}=0.5\), \({b_{3}}=0.1\), \({b_{4}}=0.6\), \({k_{1}}=0.5\), \({k_{2}}=2.9\), \({k_{3}}=0.9\), \({k_{4}}=0.95\), \({k_{5}}=0.21\), \({k_{6}}=0.7\), \(\mu=0.2\), \(\rho=0.5\), \(T=20\), \(z(0)=0.13\), and \(w(0)=5\). (a) The solution trajectory projected on \((z,w)\)-plane. (b) The corresponding time course of the number of active osteoclasts \((z)\). (c) The corresponding time course of the number of active osteoblasts \((w)\).