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Theory and Modern Applications

Figure 2 | Advances in Difference Equations

Figure 2

From: An impulsive mathematical model of bone formation and resorption: effects of parathyroid hormone, calcitonin and impulsive estrogen supplement

Figure 2

Numerical simulation of equations (4a)-(4d). The solution trajectory is bounded within a positive range as time passes. Here, all parameters are chosen to satisfy the conditions in Theorem 2, \({a_{1}}=0.2\), \({a_{2}}=0.3\), \({a_{3}}=0.21\), \({a_{4}}=0.9\), \({a_{5}}=0.4\), \({b_{1}}=0.7\), \({b_{2}}=0.5\), \({b_{3}}=0.1\), \({b_{4}}=0.3\), \({k_{1}}=0.5\), \({k_{2}}=1.9\), \({k_{3}}=0.9\), \({k_{4}}=0.9\), \({k_{5}}=0.01\), \({k_{6}}=0.75\), \(\mu=0.5\), \(\rho=0.5\), \(T=10\), \(z(0)=0.7\), and \(w(0)=3\). (a) The solution trajectory projected on \((z,w)\)-plane. (b) The corresponding time course of the number of active osteoclasts \((z)\) and (c) The corresponding time course of the number of active osteoblasts \((w)\).

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