| Citation: |
Jiazhe Lin, Ling Zhou, Zhu Zhou. FIXED-TIME SYNCHRONIZATION OF A REACTION-DIFFUSION BAM NEURAL NETWORK WITH DISTRIBUTED DELAY AND ITS APPLICATION TO IMAGE ENCRYPTION[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 1869-1892. doi: 10.11948/20220300
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FIXED-TIME SYNCHRONIZATION OF A REACTION-DIFFUSION BAM NEURAL NETWORK WITH DISTRIBUTED DELAY AND ITS APPLICATION TO IMAGE ENCRYPTION
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Abstract
In this paper, we investigate the fixed-time synchronization of reaction-diffusion BAM neural networks, where both discrete and distributed delays are taken into account. Combining Lyapunov stability theory and several integral inequalities, fixed-time synchronization criteria of master and slave systems are established. Through sensitivity analysis, we find the key controller parameters that have a great influence on the maximum settling time. Using the chaotic sequences generated by the neural network, the color image can be encrypted by the Arnold Cat Map and pixel diffusion. Experiments show that the image encryption algorithm designed in this paper has excellent properties of security and anti-attacking, which meets the requirements for the secure transmission of image information.
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References
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Jiazhe Lin, Ling Zhou, Zhu Zhou. FIXED-TIME SYNCHRONIZATION OF A REACTION-DIFFUSION BAM NEURAL NETWORK WITH DISTRIBUTED DELAY AND ITS APPLICATION TO IMAGE ENCRYPTION[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 1869-1892. doi: 10.11948/20220300
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Figure 1.
Spatiotemporal chaos of neuron states
$ u_1(t, x) $ $ u_2(t, x) $ $ v_1(t, x) $ $ v_2(t, x) $ -
Figure 2.
Phase diagrams of neuronic state variables
$ (u_1(t, 0), u_2(t, 0)) $ $ (u_1(t, 1), u_2(t, 1)) $ $ (v_1(t, 0), v_2(t, 0)) $ $ (v_1(t, 1), v_2(t, 1)) $ -
Figure 3.
Spatiotemporal dynamical behaviors of the corresponding error system.
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Figure 4.
Synchronization error states
$ e_{u1}(t, 0) $ $ e_{u2}(t, 0) $ $ e_{v1}(t, 0) $ $ e_{v2}(t, 0) $ -
Figure 5.
PRCCs of
$ T_{\max} $ $ p $ $ q $ $ {k_{12}^{(1)}} $ $ {k_{13}^{(1)}} $ $ {k_{22}^{(1)}} $ $ {k_{23}^{(1)}} $ $ {k_{12}^{(2)}} $ $ {k_{13}^{(2)}} $ $ {k_{22}^{(2)}} $ $ {k_{23}^{(2)}} $ -
Figure 6.
P-values of NIST randomness test for matrix
$ K $ -
Figure 7.
Block diagram of image encryption algorithm.
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Figure 8.
Original, encrypted and decrypted images of component R, respectively.
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Figure 9.
Histograms of original and decrypted images.
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Figure 10.
Scatter figures of original and decrypted images (R) in diagonal direction.
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Figure 11.
Adjacent pixel correlation of encrypted images in literature [5, 11] and[18].
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Figure 12.
Decryption effect under different shear attacks.
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Figure 13.
Decryption effect under different noise interference.