B

50 40 30 20 10

50 40 30 20 10

50 40 30 20 10

50 40 30 20 10

60 50 40 30 20 10

60 50 40 30 20 10

0 0.1

Figure 15 Period-halving bifurcation from chaos to cycles of system [2] with initial value X(0) = (3, 4, 5). (a) Chaos when p = 26.35; (b) phase portrait of 8T period solution for p = 26.5; (c) phase portrait of 4T period solution for p = 27.0; (d) phase portrait of 2T period solution for p = 29.0; and (e) phase portrait of quasi-T period solution for p = 30.9.

Figure 16 Crises are shown: When p is slightly increased beyond ^36.0, the chaos suddenly appears. (a) p = 36.0; (b) p = 36.000000001.

Figure 16 Crises are shown: When p is slightly increased beyond ^36.0, the chaos suddenly appears. (a) p = 36.0; (b) p = 36.000000001.

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