Figure 3

A computer simulation of Eqs. (1a)–(1d). The solution of the system is positive periodic. Here, \({a_{1}}=0.5, {a_{2}}=0.4, {b_{1}}=0.5, {r_{1}}=0.9, {d_{1}}=0.01, {d_{2}}=0.2, {h_{1}}=0.3, {h_{2}}=2\), \({h_{3}}=0.5\), \(\alpha =0.5\), \(\beta =0.5, T=5\), \(B(0)=5\), and \(C(0)=5\). Here, all conditions in Theorem 3 are satisfied. (a) The solution trajectory projected on \((B,C)\)-plane. (b) The time series of the population density of brown planthoppers \((B)\) and (c) The time series of population density of Cyrtorhinus lividipennis \((C)\)