*4.3. Effects of Changing Initial Points*

Now, we investigate the effect of changing initial points. First, we compare the system behavior when initial values have small changes in the X-axis, namely, *I*1 = (0, −0.7, 0) and *I*2 = (0.0001, −0.7, 0); see Figure 14. Next, we consider the case of small changes in the Y-axis, namely, *I*1 = (0, −0.7, 0) and *I*2 = (0, −0.7001, 0); the resulting simulation is shown in Figure 15. Finally, the effect of small changes in the Z-axis of the initial point, namely, *I*1 = (0, −0.7, 0) and *I*2 = (0, −0.7, 0.0001) is illustrated in Figure 16.

From Figures 14–16, we see that a small difference in initial points leads to a big difference in oscillations of *x*(*t*), *y*(*t*), *z*(*t*). Thus our dynamical system is highly sensitive to initial conditions, a characteristic of a chaotic system.

**Figure 13.** The trajectories of (*x*(*t*), *y*(*t*), *z*(*t*)) in 3D.

**Figure 14.** Effects of changing initial points in X-axis from *I*1 = (0, −0.7, 0) to *I*2 = (0.0001, −0.7, 0).

**Figure 15.** Effects of changing initial points in Y-axis from *I*1 = (0, −0.7, 0) to *I*2 = (0, −0.7001, 0).

**Figure 16.** Effects of changing initial points in Z-axis from *I*1 = (0, −0.7, 0) to *I*2 = (0, −0.7, 0.0001).
