Figure 2

A computer simulation of Eqs. (1a)–(1d). The solution of the system is permanent. Here, \({a_{1}}=0.5, {a_{2}}=0.7, {b_{1}}=0.5\), \({r_{1}}=0.9\), \({d_{1}}=0.01\), \({d_{2}}=0.1\), \({h_{1}}=3\), \({h_{2}}=5\), \({h_{3}}=0.2\), \(\alpha =0.2\), \(\beta =0.2, T=10\), \(B(0)=5\), and \(C(0)=5\). Here, all conditions in Theorem 2 are satisfied. (a) The solution trajectory projected on the \((B,C)\)-plane. (b) The bounded time series of the population density of brown planthoppers \((B)\). (c) The bounded time series of the population density of Cyrtorhinus lividipennis \((C)\)