Figure 3

Numerical simulation of equations (3a)-(3d). The solution trajectory approaches a limit cycle as time passes. Here, all parameters are chosen to satisfy the conditions in Theorem 6.1. Here, \({c_{1}}=0.7\), \({c_{2}}=0.2\), \({c_{3}}=0.35\), \({c_{4}}=0.9\), \({d_{1}}=0.95\), \({d_{2}}=0.005\), \({d_{3}}=0.7\), \({k_{1}}=1.2\), \({k_{2}}=0.35\), \({k_{3}}=0.9\), \({k_{4}}=3.9\), \(\mu=0.9\), \(\rho=0.1\), \(T=10\), \(y(0)=0.1\), and \(z(0)=2\). (a) The solution trajectory projected on \((y,z)\)-plane. (b) The corresponding time course of the number of active osteoclasts \((y)\) and (c) the corresponding time course of the number of active osteoblasts \((z)\) exhibiting sustained oscillation.