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Theory and Modern Applications

Figure 1 | Advances in Difference Equations

Figure 1

From: Effect of insecticide on the population dynamics of brown planthoppers and Cyrtorhinus lividipennis: a modeling approach

Figure 1

A computer simulation of Eqs. (1a)–(1d). The solution trajectory tends toward the oscillatory solution \((0,\tilde{C}(t))\) as time progresses. Here, \({a_{1}}=0.5, {a_{2}}=0.8, {b_{1}}=0.5\), \({r_{1}}=0.9\), \({d_{1}}=0.01, {d_{2}}=0.1, {h_{1}}=2, {h_{2}}=5, {h_{3}}=0.3\), \(\alpha =0.5, \beta =0.5, T=1\), \(B(0)=5\), and \(C(0)=10\). Here, all conditions in Theorem 1 are satisfied. (a) The solution trajectory projected on the \((B,C)\)-plane. (b) The time series of the population density of brown planthoppers \((B)\) tending to a vanishing level. (c) The time series of the population density of Cyrtorhinus lividipennis \((C)\) exhibiting positive oscillation

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