Figure 1

Numerical simulation of equations (4a)-(4d). The solution trajectory approaches oscillatory solution \((0,\tilde {w}(t))\) as time passes. Here, all parameters are chosen to satisfy the conditions in Theorem 1, i.e., \({a_{1}}=0.65\), \({a_{2}}=0.3\), \({a_{3}}=0.3\), \({a_{4}}=0.9\), \({a_{5}}=0.1\), \({b_{1}}=0.5\), \({b_{2}}=0.2\), \({b_{3}}=0.425\), \({b_{4}}=0.5\), \({k_{1}}=0.1\), \({k_{2}}=0.5\), \({k_{3}}=0.1\), \({k_{4}}=0.5\), \({k_{5}}=0.01\), \({k_{6}}=0.75\), \(\mu=0.1\), \(\rho=0.1\), \(T=1\), \(z(0)=0.0001\), and \(w(0)=0.0001\). (a) The solution trajectory projected on \((z,w)\)-plane. (b) The corresponding time course of the number of active osteoclasts \((z)\) tending towards zero. (c) The corresponding time course of the number of active osteoblasts \((w)\) exhibiting positive oscillation.