Initial Offset Boosting Dynamics in A Memristive Hopfield Neural Network and Its Application in Image Encryption

doi:10.19596/j.cnki.1001-246x.8547

Abstract

Abstract:

A memristive Hopfield neural network (HNN) model is proposed in which an improved multi-stable memristor is used to simulate coupled neuron synapses. Dynamical behavior of the model is analyzed and simulated with bifurcation diagram, Lyapunov exponential spectrum, phase plot and Poincare section. It shows that the memristive HNN generates chaotic attractors with different topologies and generates initial offset boosting highly dependent on initial value of the memristor. Finally, a chaotic image encryption scheme is designed based on the memristive HNN. The histogram, correlation, information entropy and key sensitivity are analyzed. It shows that the image encryption scheme resists effectively various internal and external statistical analysis attacks and has higher security.

Key words: memristor, hopfield neural network, initial offset boosting, chaos, image encryption

Liang SUN, Jia LUO, Yinhu QIAO. Initial Offset Boosting Dynamics in A Memristive Hopfield Neural Network and Its Application in Image Encryption[J]. Chinese Journal of Computational Physics, 2023, 40(1): 106-116.

Figures/Tables 15

Fig.1 Memristor v-i curve related to input signal amplitude/frequency (a) F = 0.2, pinched hysteresis loops at different amplitudes; (b) A=2, pinched hysteresis loops at different frequencies

Fig.2 Topology of memristive HNN

Fig.3 Intersections of function f1 (blue) and function f2 (red)

Table 1 Equilibrium points, eigenvalues, and stabilities of memristive HNN

线平衡点	特征值	平衡点稳定性
(0, 0, 0, 0, 0)	-1, 0.32±6.312j, 0.929 9±3.331 7j	不稳定鞍焦
(0, ±0.058 44, ±0.322 759, 0, ±3.12)	-1, 0.276 9±6.06j, 0.899 8±3.255 6j	不稳定鞍焦
(0, 0.043 198, 0.731 52, 0, ±6.24)	-1, -0.155 67±5.064 7j, 0.801 18±3.180 5j	不稳定鞍焦
(0, 0.067 25, 0.652 4, 0, ±9.36)	-1, 0.365 2±1.974 6j, 0.956 3±3.575 6j	不稳定鞍焦
(0, ±0.086 47, ±1.102 1, 0, ±12.48)	-1, 1.103 25±3.258 9j, 3.538, -5.59	不稳定鞍焦

Fig.4 Dynamical behavior related to parameter μ (a) bifurcation diagram; (b) Lyapunov exponents

Fig.5 Attractors of the memristive HNN under different parameter μ (a) chaotic attractor at μ=0.1, (b) chaotic attractor at μ=1, (c) periodic attractor at μ=1.255, (d) chaotic attractor at μ=1.5, (e) quasi-periodic attractor at μ=1.8, (f) chaotic attractor with μ=1.89

Fig.6 Bifurcation diagram about initial value φ0

Fig.7 Initial offset boosting dynamics (a) coexisting six attractors, (b) coexisting six chaotic sequences

Fig.8 Poincaré section (a) x1=0; (b) x2=0; (c) x4=0

Fig.9 Basin of attraction

Fig.10 A chaotic image encryption system

Fig.11 (a)-(c) Plain images; (d)-(f) Histograms of the plain images; (g)-(i) Encrypted images; (j)-(l) Histograms of the encrypted images

Table 2 Correlation coefficients and information entropies of original images and encrypted images

图片	水平相关系数	垂直相关系数	对角相关系数	信息裔
Lena原始图	0.970 303	0.941 693	0.925 557	7.374 0
Lena加密图	- 0.001 030	0.001 724	0.002 602	7.997 4
Peppers原始图	0.971 015	0.965 136	0.943 933	7.570 3
Peppers加密图	0.001 820	- 0.000 987	0.002 412	7.997 7
Baboon原始图	0.822 077	0.859 746	0.770 734	7.257 7
Baboon加密图	- 0.002 623	- 0.001 277 5	- 0.005 794	7.997 4

Fig.12 (b), (e), (h) Correct decryption images; (c), (f), (i) Wrong decryption images

Table 3 Test results of NPCR and UACI

	NPCR(Lena/Peppers/Baboon)	UACI(Lena/Peppers/Baboon)
Ref.[22]	99.58/--/--	33.64/--/--
Ref.[23]	99.65/99.84/--	33.64/33.68/--
Ref.[24]	99.606 3/--/99.609 4	33.295 8/--/33.328 2
本文	99.694 8/99.827 5/99.689 2	33.651 8/33.680 2/33.692 1

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