An Efficient Mathematical Approach for the Fraction Order Differentiation Based on Future Applications of Chaotic Parameter

Normalized chaotic parameters examine the characterization of the particle production fluids produced at unusual energies and investigate a remarkable behavior in quantum measurement. The analogous characterization can be analyzed to probe the chaotic systems of boson particles creating sources of extraordinary energy. We observe that the bosons appear to be the appropriate aspirants of chaos fractions, and the normalized chaotic parameters evaluate the presence of such conglomerate phases significantly. The core point of this manuscript is that we calculate and examine the normalized chaotic parameters by differential equations to analyze the characteristics of the chaotic systems and their applications in thermal as well as in mechanical engineering. With such an efficient and distinctive approach, we perceive significant consequences for the correlator at higher temperature regimes.

Tri-valued Memristor-based Hyper-chaotic System with Hidden and Coexistent Attractors

Recently, the nonlinear dynamics of memristor has attracted much attention. In this paper, a novel fourdimensional hyper-chaotic system (4D-HCS) is proposed by introducing a tri-valued memristor to the famous L¨u system. Theoretical analysis shows that the 4D-HCS has complex chaotic dynamics such as hidden attritors and coexistent attractors, and it has larger maximum Lyapunov exponent and chaotic parameter space than the original L¨u system. We also experimentally analyze the dynamics behaviors of the 4D-HCS in aspects of the phase diagram, Poincar´e mapping, bifurcation diagram, Lyapunov exponential spectrum, and the correlation coefficient, and the analysis results show the complex dynamic characteristics of the proposed 4D-HCS. In addition, the comparison with binary-valued memristorbased chaotic system shows that the 4D-HCS has unique characteristics such as hyper-chaos and coexistent attractors. To show the easy implementation of the 4D-HCS, we implement the 4D-HCS in an analogue circuit-based hardware platform, and the implementation results are consistent with the theoretical analysis. Finally, using the 4D-HCS, we design a pseudorandom number generator to explore its potential application in cryptography.

Multi-image Reorganization Encryption Based on S-L-F Cascade Chaos and Bit Scrambling

Aiming at the problems of small value range of a single chaotic parameter, low sequence chaos, and transient effects, a composite chaotic system of cascaded Sine-Sine mapping, Logistic chaos and generalized third-order Fibonacci is proposed (S-L-F). The new system is highly sensitive to initial values, the maximum spectral entropy of the generated sequence can reach 0.95, and the value range of the parameter x is expanded to [0,4] compared with the traditional Logistic, indicating that the new system is suitable for generating pseudo-random sequences for image encryption. For the problem that the traditional multi-image encryption scheme can only encrypt images of the same type and size, the practicability is poor, and a multi-image encryption scheme based on image reorganization and biting is proposed. The algorithm recombines any number, different sizes and different types of images into a three-dimensional matrix, converts it into a binary matrix, performs bit-level scrambling and surface cyclic scrambling, and then restores the scrambling matrix to decimal, and the chaotic sequence performs exclusive-or diffusion, and completes simultaneous encryption at one time, which greatly improves the encryption efficiency and scope of application. The NPCR of the ciphertext image is 0.9961, and the UACI is 0.3345, which proves that the ciphertext image can effectively resist the difference attack. The information entropy is greater than 7.999, which can effectively resist attacks. It has certain application value in image information security. Experimental analysis shows that the algorithm has high security and strong practicability.

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

A New Image Encryption Algorithm with Cantor Diagonal Scrambling Based on the PUMCML System

In this paper, a new spatiotemporal chaotic Parameter Uncertainty Mixed Coupled Map Lattice (PUMCML) is proposed. The Cantor diagonal matrix is generated from the Cantor set, and the ordered rotation scrambling strategy for this matrix is used to generate the scrambled image. Cantor set is a fractal system, so the Cantor set has a good effect on chaotic image encryption. The dynamic behavior of the PUMCML system is analyzed. The system has good chaotic property, so it is very suitable for chaotic image encryption. Using the PUMCML system, a diffusion strategy based on the mixture of Arnold and Logistic is proposed. Compared with other algorithms, the encryption effect of the proposed method is better and more secure.

Image Encryption Algorithm Based on Tent Delay-Sine Cascade with Logistic Map

We propose a new chaotic map combined with delay and cascade, called tent delay-sine cascade with logistic map (TDSCL). Compared with the original one-dimensional simple map, the proposed map has increased initial value sensitivity and internal randomness and a larger chaotic parameter interval. The chaotic sequence generated by TDSCL has pseudo-randomness and is suitable for image encryption. Based on this chaotic map, we propose an image encryption algorithm with a symmetric structure, which can achieve confusion and diffusion at the same time. Simulation results show that after encryption using the proposed algorithm, the entropy of the cipher is extremely close to the ideal value of eight, and the correlation coefficients between the pixels are lower than 0.01, thus the algorithm can resist statistical attacks. Moreover, the number of pixel change rate (NPCR) and the unified average changing intensity (UACI) of the proposed algorithm are very close to the ideal value, which indicates that it can efficiently resist chosen-plain text attack.

Pseudorandom Number Generator (PRNG) Design Using Hyper-Chaotic Modified Robust Logistic Map (HC-MRLM)

Robust chaotic systems, due to their inherent properties of mixing, ergodicity, and larger chaotic parameter space, constitute a perfect candidate for cryptography. This paper reports a novel method to generate random numbers using modified robust logistic map (MRLM). The non-smooth probability distribution function of robust logistic map (RLM) trajectories gives an un-even binary distribution in randomness test. To overcome this disadvantage in RLM, control of chaos (CoC) is proposed for smooth probability distribution function of RLM. For testing the proposed design, cryptographic random numbers generated by MRLM were vetted with National Institute of Standards and Technology statistical test suite (NIST 800-22). The results showed that proposed MRLM generates cryptographically secure random numbers (CSPRNG).

Enhancing Ikeda Time Delay System by Breaking the Symmetry of Sine Nonlinearity

In the present contribution, an asymmetric central contraction mutation (ACCM) model is proposed to enhance the Ikeda time delay system. The modified Ikeda system model is designed by introducing a superimposed tanh function term into the sine nonlinearity term. Stability and Hopf bifurcation characteristics of the system are analyzed theoretically. Numerical simulations, carried out in terms of bifurcation diagrams, Lyapunov exponents spectrum, phase portraits, and two-parameter (2D) largest Lyapunov exponent diagrams are employed to highlight the complex dynamical behaviors exhibited by the enhanced system. The results indicate that the modified system has rich dynamical behaviors including limit cycle, multiscroll hyperchaos, chaos, and hyperchaos. Moreover, as a major outcome of this paper, considering the fragile chaos phenomenon, the ACCM-Ikeda time delay system has better dynamical complexity and larger connected chaotic parameter spaces (connectedness means that there is no stripe corresponding to nonchaotic dynamics embedded in the chaos regions).

WFRFT Secure Communication Method Based on Chaotic Parameter Pool

In this study, to solve the hidden limitation of conventional weighted fractional Fourier transform (WFRFT), a random modulation order parameter pool is established by applying chaos technology. Further, a WFRFT secure communication method based on the chaotic parameter pool (CPP) is proposed. Based on the effective characteristics of tent mapping and the sequence output range, the parameter pool constructor is established by parameter transformation. Furthermore, for each parameter selection period, the information can be processed by WFRFT using different modulation orders. The modeling and simulation demonstrate that this method can significantly increase the bit error rate and processing time of unauthorized receivers. This indicates that it can greatly increase the scanning difficulty of unauthorized users and improve the concealment and security of the original information transmission.