INPUT at 
wi # gunna ) 
=i ‘ iti | all Wi, 
1G 00 100.00 200.00 300.00 400. ~ 500.00 600.00 700.00 800.00 900.00 1000.00 
Tt 
i 
Ht 
OUTPUT X 
4.00 
0 0.00 
4.0 
0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00 
—e t 
Fig. 13.5. X, = (1.5+0.286%) X,,-0.96X0+a,, 
Input a, = sin{2x f(t) - t: Kf) is decreasing by time. 
(From Ozaki.98). 
As an example, Ozaki showed that, for a model 
X, = (1.95 + 0.23 e-%1) X,1- (0.96 + 0.24 eX) Xin+€;, (13.53) 
the characteristic roots are Ag = 1.09 + 0.109i and A~ =0.975 + 0.0968i, and LX!? 
actually moves between lol? = 1.20 to U.|* = 0.96, which shows Van del Pol type 
oscillation, as shown schematically in Fig. 13.6. Figure 13.7 shows that the model 
without €,, which starts with different initial values, approaches to the same limit period. 
Thus this shows that the model expressed by Eq. 13.53 has a stable limit period. 
Fig. 13.6. 1(0),A(«) for Van del Pol type model. 
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