Fig. 1. Lyapunov exponent diagram.

Fig. 2. Bifurcation diagram of system (2) variation with .

Fig. 3. Time series diagram: (a) time series; (b) time series; (c) time series; (d) time series; (e) time series

Fig. 4. Three-dimensional phase diagram: (a) Three-dimensional map; (b) Three-dimensional map; (c) Three-dimensional map; (d) Three-dimensional map; (e) Three-dimensional map; (f) Three-dimensional map; (g) Three-dimensional map; (h) Three-dimensional map; (i) Three-dimensional map; (j) Three-dimensional map.

Fig. 5. Two-dimensional plane phase diagram: (a) flat; (b) flat; (c) flat; (d) flat; (e) flat; (f) flat; (g) flat.

Fig. 6. Digital image encryption and decryption experiment: (a) Original Lena image; (b) encrypted Lena image; (c) decrypted Lena image; (d) original baboon image; (e) encrypted baboon image; (f) decrypted baboon image; (g) original boat image.; (h) encrypted boat image; (i)decrypted boat image.

Fig. 7. Histogram of plaintext and ciphertext images (a) Plaintext Lena image histogram; (b) ciphertext Lena image histogram; (c) plaintext baboon image histogram; (d) ciphertext baboon image histogram; (e) plaintext boat image histogram; (f) ciphertext boat image histogram.

Fig. 8. Key sensitivity tests: (a) Plain-image; (b) cipher with key ; (c) cipher with key ; (d) right decrypted ; (e) decrypted with ; (f) decrypted with .

Fig. 9. Correlation analysis chart in three directions before and after baboon image encryption: (a), (b) Diagonally adjacent; (c), (d) horizontally adjacent; (e), (f) vertically adjacent.

Fig. 10. Anti-shear attack capability analysis chart: (a) Ciphertext before cutting; (b) ciphertext after cutting; (c) decrypted image before cutting; (d) decrypted image after cutting.

Fig. 11. Anti-noise attack capability analysis chart: (a) Ciphertext before adding noise; (b) ciphertext after adding noise; (c) decrypted image before adding noise; (d) decrypted image after adding noise.