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Rebalancing 125 where o2 is analogous to 1. Analogously, we can get a full model of the species in Population 2 via (=2(1-n2+an Without the species in Population 2, milkfish will disappear; we set their death rate as T3. The species in Population 2 provide food for the milkfish and the growth of milkfish is also restricted by internal blocking action Here the model is i(t)=T33 +a4忑2 Summarizing, we have simultaneous equations constituting aninterdepen- dent mathematical model for the three populations i1(t)=x1r1 101 N, 十σ ()=T3a3( N34 N2 We obtain the values of some parameters in the model, and through onlinear data fitting of the original data of the local three populations [Shan and Tang 2007; Sumagaysay-Chavoso 1998; Chen and Chou 2001], we get their natural growth rates 05, a3=0.5 N1=150×103,N2=30×103,N3=22×103 According to the volume of local fish pens and relevant materials, we get the original numbers of the three populations z1(0)=1215×103,x2(0)=27×103,x3(0) Then we use Matlab to implement the model, with the results of Figure 2, where we see that can see that with the passage of time, the sit)tend to the steady-state values 69, 027, 27, 015, and 1, 760 The number 27, 015 of the species in Population 2 is made up of herbiv- orous fish, molluscs, crustaceans, and echinoderms. Now we confirm the numbers of all the species in Population 2, which stay at the same trophic level, coexisting and mutually competingRebalancing 125 where 0-2 is analogous to 01. Analogously, we can get a full model of the species in Population 2 via t2(t) = r2x2 -1 - f + 0*2f - 0'3 • Without the species in Population 2, milkfish will disappear; we set their death rate as r3 . The species in Population 2 provide food for the milkfish, and the growth of milkfish is also restricted by internal blocking action. Here the model is b3 (t) = r3x 3 X3 + Or4 • Summarizing, we have simultaneous equations constituting an interdepen￾dent mathematical model for the three populations: *ti(t) = x 1 r, 1 ( - 0-1 , X2(t) = r2X2 -1 - 2+ U2 - U3 , 'b3(t) = r3X3 - I - -X3 + U-4 X2 We obtain the values of some parameters in the model, and through nonlinear data fitting of the original data of the local three populations [Shan and Tang 2007; Sumagaysay-Chavoso 1998; Chen and Chou 2001], we get their natural growth rates: u,i = 0.6, u"2 = 0.5, o-3 0.5, o"4= 2; N, = 150 x 10 3, N 2 = 30 x 10 3 , N 3 = 2.2 x 10 3 . According to the volume of local fish pens and relevant materials, we get the original numbers of the three populations: xi(0) = 121.5 x 103, x 2 (0) = 27 x 103, x3 (0) = 2 x 103. Then we use Matlab to implement the model, with the results of Figure 2, where we see that can see that with the passage of time, the xi (t) tend to the steady-state values 69,027, 27,015, and 1,760. The number 27,015 of the species in Population 2 is made up of herbiv￾orous fish, molluscs, crustaceans, and echinoderms. Now we confirm the numbers of all the species in Population 2, which stay at the same trophic level, coexisting and mutually competing
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