Introduction to Hybrid Intelligent Networks by Zhi-Hong Guan & Bin Hu & Xuemin (Sherman) Shen

Author:Zhi-Hong Guan & Bin Hu & Xuemin (Sherman) Shen
Language: eng
Format: epub
ISBN: 9783030021610
Publisher: Springer International Publishing

Fig. 5.4Chaotic behaviors and synchronization of four-dimensional NNs (5.27): Example 5.2, τ a = 0.12. (a) Chaotic trajectories of single NN: x i1 and x i2. (b) Chaotic trajectories of single NN: x i3 and x i4. (c) State trajectories of interconnected NNs: x i1 and x i2. (d) State trajectories of interconnected NNs: x i3 and x i4. (e) Long-term state trajectories of interconnected NNs: x i1 and x i2. (f) Long-term state trajectories of interconnected NNs: x i3 and x i4

In this example, the coupling matrix G, the nonlinear protocol (5.4), and the randomized broadcast impulse (5.6) are as given in Example 5.1. Choosing ω k = 3.5, one gets β k = 1.0417 in (5.17). The randomized impulse (5.29) is then an impulsive perturbation. Similarly for condition (5.18), one has α 2 = 2.8371 and α = 4.4190. Since , β = 1.0417, τ a = 0.12, and , , then condition (5.19) holds. The initial states are randomly chosen: 5 ∗randn(12, 1). The impulsive state trajectories of NNs (5.27) are presented in Fig. 5.4c–f. The synchronization errors are compared in Fig. 5.5: impulse versus no-impulse, with T syn = 6.8451(s) and T syn0 = 1.2187(s). In particular, the state impulses of NNs (5.27) that given in Examples 5.1 and 5.2 are respectively shown in Fig. 5.6a and Fig. 5.6b, c.

Fig. 5.5Error comparison: perturbative impulse, Example 5.2

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