A Novel Four-wing Chaotic System And Its Image Encryption Applicatio

Chaos as a unique pseudo-random state of motion in nonlinear dynamics is a phenomenon found in different disciplines and fields.The current research on chaotic systems is mainly to construct some chaotic and hyperchaotic systems with rich dynamic properties to enrich the chaos theory and its application research,mainly including memristive chaotic systems,multi-wing chaotic systems and hidden chaotic systems.In recent years,the discovery of hidden attractors has made the study of hidden chaos systems a hot topic in chaos research.The chaotic systems obtained by combining multi-wing chaotic systems and hidden chaotic systems have more complex dynamical behaviors,which are important for the study of chaos theory and have potential engineering applications.In this paper,two new multi-wing chaotic systems are proposed based on the 3-D Sprott system,which have self-excited attractor and hidden attractor properties,respectively.For the chaotic system with self-excited attractor,the chaotic properties of the system are confirmed by Poincarémapping and LEs;the parameter sensitivity is analyzed by using bifurcation diagrams and LEs,and the system is found to enter chaos through double periodic bifurcation;the double periodic and chaotic signals of the system are confirmed by power spectra,and the system is also found to have a wide chaotic region as the parameter c varies.In this system,the attractor asymmetric coexistence phenomenon exists,and the generated bipolar signal can be converted to unipolar signal by offset increment,which is convenient for subsequent engineering applications.A corresponding simulation circuit is designed for the system to confirm the correctness of the numerical analysis,and the experimental results of the hardware circuit are in good agreement with the numerical analysis.In terms of multi-wing chaos with hidden attractors,the theoretical analysis reveals that the system has no equilibrium point and has hidden attractor properties.The hidden extreme multistability of the system is analyzed using the attractor basin,and a variety of attractor coexistence phenomena can be observed,mainly including chaotic,quasi-periodic,period 2 and period 1 attractor coexistence.Four transient transition phenomena are also found in this system,and the transient transition phenomena are confirmed by time domain waveforms,2-D phase portraits and LE analysis.Finally,the corresponding simulation circuit is designed based on this system,and the experimental results are basically consistent with the numerical simulation analysis,providing conditions for practical engineering applications.For the four-wing chaotic system proposed in Chapter 2,the image encryption and decryption of color images are studied using the encryption algorithm combining dislocation and diffusion operations.The encryption effect is analyzed by comparing the histogram,sensitivity,secret key space,correlation coefficient and information entropy of the original image with the encrypted image.The analysis results show that the range correlation of the encrypted image is 0±0.02,its pixel point distribution is highly discrete and extremely sensitive to the initial conditions(10^-18),and the encryption scheme has a large secret key space(6.7×10¹¹⁵).