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大量动物实验表明, 生物神经系统中存在着不规则的混沌现象. 混沌神经网络是一种高度非线性动力系统, 它可以实现一系列复杂的动力学行为, 能够优化全局搜索和神经计算, 还可产生伪随机序列进行信息加密. 基于脑波由不同频率的正弦信号叠加理论, 为使神经网络更具生物特性, 提出了一种基于多频-变频正弦函数和分段型函数的非单调激活函数. 分析表明, 通过调节参数可使该激活函数拥有不同状态的脑电信号, 能够模拟频率不同、类型不同的脑电波同时工作时丰富多变的脑部活动. 基于该激活函数设计了一种新型混沌细胞神经网络. 采用基于结构复杂度的SE复杂度算法和C0复杂度算法分析了神经网络的复杂度; 利用Lyapunov指数谱、分岔图和吸引盆等方法, 详细分析了激活函数参数变化对其动力学特性的影响, 发现此混沌神经网络模型出现了一系列的复杂现象, 如多种不同类型的混沌吸引子、共存混沌吸引子、共存极限环等, 提升了混沌神经网络的性能, 证明了多频正弦混沌神经网络具有丰富的动力学特性, 使得其在信息处理、信息加密等方面也具有较好的前景.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 下载:
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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}}}$ 下载:
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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}}}$ 下载:
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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)下载:
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