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A large number of animal experiments show that there is irregular chaos in the biological nervous systems. An artificial chaotic neural network is a highly nonlinear dynamic system, which can realize a series of complex dynamic behaviors, optimize global search and neural computation, and generate pseudo-random sequences for information encryption. According to the superposition theory of sinusoidal signals with different frequencies of brain waves, a non-monotone activation function based on the multifrequency-frequency conversion sinusoidal function and a piecewise function is proposed to make a neural network more consistent with the biological characteristics. The analysis shows that by adjusting the parameters, the activation function can exhibit the EEG signals in its different states, which can simulate the rich and varying brain activities when the brain waves of different frequencies and types work at the same time. According to the activation function we design a new chaotic cellular neural network. The complexity of the chaotic neural network is analyzed by the structural complexity based SE algorithm and C0 algorithm. By means of Lyapunov exponential spectrum, bifurcation diagram and basin of attraction, the effects of the activation function’s parameters on its dynamic characteristics are analyzed in detail, and it is found that a series of complex phenomena appears in the chaotic neural network, such as many different types of chaotic attractors, coexistent chaotic attractors and coexistence limit cycles, which improves the performance of the chaotic neural network, and proves that the multi-frequency sinusoidal chaotic neural network has rich dynamic characteristics, so it has a good prospect in information processing, information encryption and other aspects.
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类型 频率/Hz ${\varepsilon _1}$(0) ${\varepsilon _2}$(0) $\delta $ 0.50—3.01 0.32 0.64 $\theta $ 3.98—6.97 0.04 0.08 $\alpha $ 7.96—15.09 0.02 0.04 $\beta $ 15.92—30.18 0.01 0.02 $\gamma $ 36.17—100.31 0.0044 0.0088 
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参数 参数值 参数 参数值 参数 参数值 参数 参数值 S13 –1.0 S41 98 S65 4.0 m 10.6 S14 –1.0 S44 –105 S66 –4.0 n 0.1 S22 –1.3 S51 1.0 A24 5.0 ${\varepsilon _1}$ 0.04 S23 2.0 S52 18 A 0.5 ${\varepsilon _2} $ 0.02 S31 13.0 S55 –1 c 0.25 φ $ - {{\text{π}} / {{4}}} $ S32 –14.0 S62 100 q –1.0 DownLoad:
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参数 参数值 参数 参数值 A24 5 ${\varepsilon _1}$ 0.04 A 0.5 ${\varepsilon _2}$ 0.02 m 10.6 φ $ - {{\text{π}} / {\rm{4}}}$ DownLoad:
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参数 参数值 参数 参数值 A24 5 q –1 A 0.5 ${\varepsilon _1}$ 0.04 m 5.6 ${\varepsilon _2}$ 0.02 n 2.5 φ $ - {{\text{π}} / {\rm{4}}}$ DownLoad:
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性质 类型 初始条件 混沌吸引子与
混沌吸引子Ic型、
IIc型(0.2, 0.2, 0.3, 0.4, 0.5, 0.6),
(0.52, 0.2, 0.3, 0.4, 0.5, 0.6)Ic型、
IIIc型(0.2, 0.2, 0.3, 0.4, 0.5, 0.6),
(–0.5, –1.2, 0.3, 0.4, 0.5, 0.6)IIc型、IIIc型 (0.52, 0.2, 0.3, 0.4, 0.5, 0.6),
(–0.5, –1.2, 0.3, 0.4, 0.5, 0.6)混沌吸引子
与极限环IIc型、Ip型 (0.82, 1.5, 0.3, 0.4, 0.5, 0.6),
(5.5, 5.81, 0.305, 0.4, 0.5, 0.6001)IIIc型、IIp型 (–0.8, –1.5, 0.3, 0.4, 0.5, 0.6),
(0.1, –1.51, 0.3, 0.4, 0.5, 0.6)极限环与
极限环Ip型、IIp型 (5.5, 5.81, 0.305, 0.4, 0.5, 0.6001),
(0.1, –1.51, 0.3, 0.4, 0.5, 0.6)DownLoad:
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