本文透過增加兩個非線性彈簧在主動隔振系統，進而產生一個新的主動隔振系統。我們運用創新的方法來分析及呈現主動隔振系統的3D相圖及其投影圖，使我們對於主動隔振系統有更清楚的了解。我們還通過應用各種技術來討論主動隔振系統的動力學行為。這些技術包括相圖，Poincare map，散度分析，頻譜分析，分歧圖和Lyapunov指數圖。在控制理論部分，通過應用GYC部分區域穩定理論，主動隔振系統的主動牽制控制同步完成。利用TS模糊理論的主動隔振系統的同步控制提出，並實現模糊電路。此外，採用主動隔振系統的圖像加密演算法已經實現。在這項研究中，我們還討論了直方圖分析，相關係數分析，信息熵分析和差分分析。

The chaotic system is presented in this study by adding two nonlinear springs to the active vibration isolation system which is discovered by Li et al in 2012. We use an innovative technique to present the 3-dimensional phase portraits and its projection simultaneously in order to have a better understanding of the active vibration isolation system. We also discuss the dynamical behaviors of the active vibration isolation system by applying various techniques. These techniques include phase portraits, Poincare maps, divergence computing, power spectrum analysis, bifurcation diagrams and Lyapunov exponent diagrams. In the part of control theory, by applying GYC partial region stability theory, active pinning control synchronization of the active vibration isolation system is accomplished. The synchronization of active vibration isolation system using T-S fuzzy theory is proposed, and the synchronizations electric circuit is achieved. In addition, an Image encryption algorithm using active vibration isolation system is achieved. We also discuss histogram analysis, correlation analysis, information entropy analysis and differential attack analysis in this study.

[1] Lorenz, E. N. (1963). "Deterministic non-periodic flows." Journal of The Atmospheric Sciences 20: 130-141.
[2] SABIN, G. C. W. and D. SUMMERS (1993). "Chaos in a Periodically Forced Predator-PreyEcosystem Model." MATHEMATICAL BIOSCIENCES 113: 91-113.
[3] Yun, W. (2005). "High-gain observer for chaotic synchronizationand secure communication." Int. J. Commun. 18: 487–500.
[4] Wang, X. and J. Zhang (2006). "Chaotic secure communication based on nonlinear autoregressive filter with changeable parameters." Physics Letters A 357(4-5): 323-329.
[5] Iannelli, L., et al. (2008). "Subtleties in the averaging of a class of hybrid systems with applications to power converters." Control Engineering Practice 16(8): 961-975.
[6] Lu, W.-G., et al. (2008). "Filter based non-invasive control of chaos in Buck converter." Physics Letters A 372: 3217–3222.
[7] Cang, S., et al. (2009). "A four-wing hyper-chaotic attractor and transient chaosgenerated from a new 4-D quadratic autonomous system." Nonlinear Dynamics 59: 515-527.
[8] Kazantzis, N., et al. (2009). "A new model reduction method for nonlinear dynamicalsystems." Nonlinear Dynamics 59: 183-194.
[9] Song, A., et al. (2009). "Design 2D nonlinear system for information storage." Chaos, Solitons & Fractals 41(1): 157-163.
[10] Ma, J., et al. (2010). "A time-varying hyperchaotic system and its realization in circuit." Nonlinear Dynamics 62(3): 535-541.
[11] Lou, J.-J., Zhu, S.-J., He, L., Yu, X. (2005). "Application of chaos method to line spectra reduction." Journal of Sound and Vibration 286, 3645-3652.
[12] Li, Z., et al. (2012). "Research on active vibration isolation based on chaos synchronization." ICCIP 2012 Part I, CCIS 288: 9-19.
[13] Ott, E., et al. (1990). "Controlling chaos." Physical Review Letters 64(11): 1196-1199.
[14] Chen, H.-H. (2009). "Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control." Chaos, Solitons & Fractals 40(1): 466-473.
[15] Chen, H.-H. (2008). "Stability criterion for synchronization of chaotic systems using linear feedback control." Physics Letters A 372(11): 1841-1850.
[16] Chen, M. and Z. Han (2003). "Controlling and synchronizing chaotic Genesio system via nonlinear feedback control." Chaos, Solitons & Fractals 17(4): 709-716.
[17] Yau, H.-T. (2004). "Design of adaptive sliding mode controllerfor chaos synchronization with uncertainties." Chaos, Solitons and Fractals 22: 341–347.
[18] Yassen, M. T. (2007). "Controlling, synchronization and tracking chaotic Liu system using active backstepping design." Physics Letters A 360(4-5): 582-587.
[19] Feng, G. and G. Chen (2005). "Adaptive control of discrete-time chaotic systems: a fuzzy control approach." Chaos, Solitons & Fractals 23(2): 459-467.
[20] Yang, C.-H. and Z.-M. Ge (2011). "Controlling Hyperchaos and Chaotic Projective Hybrid Synchronization with Time Delay in a Three Positive Lyapunov Exponents of New Four Dimensions Chen System by Adaptive Control." Journal of Computational and Theoretical Nanoscience 8(11): 2245-2254.
[21] Paulfredeiuckson, et al. (1983). "The lyapunov dimension of strange attractors." Journal of Differential Equations 49: 185-207.
[22] Pan, L., et al. (2010). "A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems." Nonlinear Dyn 62: 417-425.
[23] Pan, L., et al. (2013). "Synchronization of Three-Scroll Unified Chaotic System (TSUCS) and its hyper-chaotic system using active pinning control." Nonlinear Dyn 73: 2059-2071.
[24] Wang, Y. W., et al. (2003). "LMI-based fuzzy stability and synchronization of Chen’s system." Physics Letters A 320: 154-159.
[25] Li, S. Y., et al. (2012). "Chaotic motions in the real fuzzy electronic circuits." Abstract and Applied Analysis, vol. 2013, Article ID 875965, 8 pages.
[26] Tanaka, K. and Wang, H. O. (2001). "Fuzzy control systems design and analysis: a linear matrix inequality approach." Wiley, New York.
[27] Zhang, W., et al. (2013). "An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion." Commun Nonlinear Sci Numer Simulat 18: 2066-2080.
[28] Wang, X. and Luan, D. (2013). "A novel image encryption algorithm using chaos and reversible cellular automata." Commun Nonlinear Sci Numer Simulat 18: 3075-3085.
[29] Nasir, Q. and Abdlrudha, H. H. (2012). "High security nested PWLCM chaotic map bit-level permutation based image encryption." Int. J. Communications, Network and System Sciences: 548-556.
[30] Wang, Y., et al. (2011). "A new chaos-based fast image encryption algorithm." Applied Soft Computing 11: 514–522.
[31] Song, C. Y., et al. (2013). "An image encryption scheme based on new spatiotemporal chaos." Optik 124: 3329-3334.
[32] Fu, C., et al. (2011). "A novel chaos-based bit-level permutation scheme for digital image encryption." Optics Communications 284: 5415-5423.
[33] Armand Eyebe Fouda, J. S., et al. (2014). "A fast chaotic block cipher for image encryption." Commun Nonlinear Sci Numer Simulat 19: 578-588.
[34] Li, J. and Liu, H. (2013). "Color image encryption based on advanced encryption standard algorithm with two-dimensional chaotic map." IET Inf. Secur., vol. 7, Iss. 4: 265-270.
[35] Shannon, C. E. (1949). "Communication theory of secrecy system." Bell Syst. Tech. J 28: 656-715.
[36] Shannon, C. E. (1948). "A mathematical theory of communication." Bell Syst. Tech. J 27: 379-423, 623-656.
[37] Ge, Z. M., et al. (1994). "Stability on partial region in dynamics." vol. 15, Iss. 2: 140-151.