磁控忆阻器耦合Hindmarsh-Rose神经元模型及其在DNA图像加密中的应用

doi:10.19596/j.cnki.1001-246x.8850

摘要/Abstract

摘要：

提出一种磁控忆阻器模型, 建立磁感应耦合Hindmarsh-Rose(HR)神经元模型。通过分岔图、李雅普诺夫指数谱、相位图以及时序图对所构建的神经元模型进行非线性动力学分析, 进而将模型所产生的混沌序列应用于DNA混沌图像加密算法。实验结果表明: 这种电磁感应HR神经元模型在磁感应强度的影响下能够产生多种放电模式和复杂的混沌行为, 并且基于该模型产生的混沌序列具有随机性, 初值敏感性, 遍历性等特点, 应用于混沌图像加密算法中具有较强的安全性。为理解神经元隐藏动力学机制和构建忆阻器神经元网络提供支持, 对神经元相关的病变治疗具有价值。

关键词: 忆阻器, Hindmarsh-Rose神经元, DNA序列, 混沌图像加密

Abstract:

Memristor coupled neurons have complex nonlinear dynamic behavior and have been widely used in neural computing and chaotic systems. In this paper, a new magnetic controlled memristor model is proposed, and the Hindmarsh-Rose(HR) neuron model is established. The neural model is analyzed by bifurcating diagram, Lyapunov exponent spectrum, phase diagram and time series diagram. Then the chaotic sequence generated by the model is applied to the DNA chaotic image encryption algorithm. The experimental results show that this HR neuron model can generate multiple discharge modes and complex chaotic behavior under the influence of magnetic induction intensity, and the generated chaotic sequences based on the model have the characteristics of randomness, initial value sensitivity, ergodic, etc., which has strong security when applied to chaotic image encryption algorithms. These results will provide strong support for understanding the dynamics of neuron hiding and constructing memristor neural network, and have great application value for the treatment of neuron-related lesions.

Key words: memristor, Hindmarsh-Rose neurons, DNA sequence, chaotic image encryption

赵益波, 杨清, 于程程, 刘明华. 磁控忆阻器耦合Hindmarsh-Rose神经元模型及其在DNA图像加密中的应用[J]. 计算物理, 2025, 42(2): 232-242.

Yibo ZHAO, Qing YANG, Chengcheng YU, Minghua LIU. Novel Magnetron Memristor Coupled Hindmarsh-Rose Neuron Model and Its DNA Image Application in Encryption[J]. Chinese Journal of Computational Physics, 2025, 42(2): 232-242.

图/表 12

图1 忆阻器的紧磁滞回线(a)f=1 Hz时不同幅度下的紧磁滞回线; (b)A=1 V时不同频率下的紧磁滞回线

Fig.1 Memristor tight hysteresis loop (a) pinched hysteresis at different amplitudes with f=1 Hz; (b) pinched hysteresis loops at different frequencies with A=1 V

图2 磁感应强度参数k∈(0.2, 1.8)变化时的动力学状态分布(a)分岔图；(b)李雅普诺夫指数谱

Fig.2 Dynamic state distribution with change of k∈(0.2, 1.8) (a) bifurcation diagram; (b) Lyapunov exponents

图3 不同磁感应强度k的吸引子和对应的膜电位时序图(a)吸引子，k=0.6; (b)膜电位时序图，k=0.6;(c)吸引子，k=1.2; (d)膜电位时序图，k=1.2; (e)吸引子，k=1.6; (f)膜电位时序图，k=1.6

Fig.3 Time series diagram of attractors and corresponding membrane potential for different magnetic induction intensities k (a) attractor with k=0.6; (b) potential sequence diagram with k=0.6; (c) attractor with k=1.2; (d) potential sequence diagram with k=1.2; (e) attractor with k=1.6; (f) potential sequence diagram with k=1.6

表1 DNA编码解码方式

Table 1 DNA encoding and decoding methods

	1	2	3	4	5	6	7	8
A	00	00	01	01	10	10	11	11
T	11	11	10	10	01	01	00	00
G	01	10	00	11	00	11	01	10
C	10	01	11	00	11	00	10	01

图4 混沌DNA图像加密流程

Fig.4 Chaotic DNA image encryption process

图5 实验结果图(a)原始图像；(b)密文图像；(c)解密图像

Fig.5 Experimental result diagram (a) original image; (b) ciphertext image; (c) decrypted image

图6 直方图(a)原始图像；(b)加密图像

Fig.6 Histogram of (a) original image and (b) encrypted image

表2 Pepper图像相关系数

Table 2 Correlation coefficients of Pepper images

算法	水平	垂直	对角线	平均值
原始图像	0.977 2	0.977 5	0.954 5	0.969 7
本文	-0.002 4	-0.009 5	0.003 6	0.005 2
Ref.[33]	0.016 8	0.044 5	-0.002 2	0.021 2
Ref.[34]	0.002 8	0.009 6	0.006 2	0.006 2
Ref.[35]	0.014 0	0.014 3	0.014 6	0.014 3
Ref.[36]	0.007 8	0.005 8	-0.016 4	0.010 0

表3 原始图像与密文图像信息熵

Table 3 Information entropy between original image and ciphertext image

通道	R	G	B
原始图像	7.268 2	7.590 1	6.995 1
加密图像	7.999 3	7.999 3	7.999 3

图7 加入不同密度椒盐噪声的解密图像，密度为(a) 0.005；(b) 0.01；(c) 0.05；(d) 0.1

Fig.7 Decrypted images of added salt and pepper noise with different densities (a) 0.005; (b) 0.01; (c) 0.05; (d) 0.1

图8 遮挡攻击实验结果(a) 数据丢失1/16; (b) 数据丢失1/8; (c)数据丢失1/4; (d)数据丢失1/2; (e)图(a)的解密结果；(f) 图(b)的解密结果; (g) 图(c)的解密结果; (h) 图(d)的解密结果

Fig.8 Experimental results of occlusion attack (a) data loss 1/16; (b) data loss 1/8 of encrypted images; (c) data loss 1/4;(d) data loss 1/2 s; (e) decryption of figure (a); (f) decryption of figure (b); (g) decryption of figure (c); (h) decryption of figure (d)

表4 不同算法的时间

Table 4 Time of different algorithms

算法	图像	加密时间/s
本文	Pepper	2.577 2
Ref.[37]	Babbon	5.785 5
Ref.[38]	Lena	9.182 7
Ref.[39]	Lena	4.392 0

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