In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing ...interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors.
The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters.
This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
The substitution box (S-box) is an important component in block encryption algorithms. In this Letter, the problem of constructing S-box is transformed to a Traveling Salesman Problem and a method ...for designing S-box based on chaos and genetic algorithm is proposed. Since the proposed method makes full use of the traits of chaotic map and evolution process, stronger S-box is obtained. The results of performance test show that the presented S-box has good cryptographic properties, which justify that the proposed algorithm is effective in generating strong S-boxes.
► The problem of constructing S-box is transformed to a Traveling Salesman Problem. ► We present a new method for designing S-box based on chaos and genetic algorithm. ► The proposed algorithm is effective in generating strong S-boxes.
•The proposed algorithm uses a new 6-D hyper-chaotic system.•Employs bit-level permutation and DNA encoding to strengthen the security of the cryptosystem in proposed algorithm.•The bit-level ...permutation is not dependent on chaotic sequence.•This proposed algorithm uses four DNA operations.
Many chaos-based image encryption algorithms using low-dimensional chaotic mapping and permutation diffusion structures have been proposed recently. However, low-dimensional chaotic maps are less secure than high-dimensional chaotic systems. Furthermore, the permutation process is independent of the plaintext and diffusion process. As a result, they are not very resistant to chosen plaintext attacks and chosen ciphertext attacks. In this paper, we propose a hyper-chaos-based image encryption algorithm that uses a 6-dimensional hyperchaotic system; the key stream generated by hyperchaotic system is related to the plaintext image. Then, bit-level permutation is employed to strengthen the security of the cryptosystem. Finally, DNA coding and operations are employed to change pixels. Theoretical analysis and numerical simulations demonstrate that the proposed algorithm is safe and reliable for image encryption.
This letter proposes a general and effective decoupled technique for the stochastic simulation of nonlinear circuits via polynomial chaos. According to the standard framework, stochastic circuit ...waveforms are still expressed as expansions of orthonormal polynomials. However, by using a point-matching approach instead of the traditional stochastic Galerkin method, a transformation is introduced that renders the polynomial chaos coefficients decoupled and therefore obtainable via repeated non-intrusive simulations and an inverse linear transformation. As discussed throughout the letter, the proposed technique overcomes several limitations of state-of-the-art methods. In particular, the scalability is hugely improved and tens of random parameters can be simultaneously treated within the polynomial chaos framework. Validating application examples are provided that concern the statistical analysis of microwave amplifiers with up to 25 random parameters.
Stochastic transmission line (TL) analysis is often challenging due to the difficulty of fully identifying the probability distributions of all randomly varying parameters, especially in the presence ...of noise. These problems cannot be directly addressed by the existing polynomial chaos expansion (PCE) framework. To overcome the limitations, this paper proposes an improved PCE method for analyzing the stochastic TL model with noise. A regression-based non-intrusive approach termed least squares polynomial chaos regression (LSPCR) is employed to determine the PCE coefficients. Six algorithms for LSPCR are developed by respectively combining three sampling strategies, i.e., standard sampling (SS), asymptotic sampling (AS), and coherence-optimal sampling (COS), with two types of norm problems: the least-squares optimization problem (LSO) and the l1-minimum problem (l1-M). Numerical experiments are conducted on noiseless and noisy problems. The results reveal that the LSO-based algorithms (LSOs) are much faster than the l1-M-based algorithms (l1-Ms), regardless of the sampling strategy. In the absence of noise, these six algorithms require only a relatively small number of samples to achieve higher accuracy in solution moments compared to the Stochastic Galerkin (SG) method. When the sample size is large, the AS-based algorithms (ASs) and the COS-based algorithms (COSs) yield more accurate results than the SS-based algorithms (SSs), regardless of the norm problems. In the presence of noise, the LSOs outperform the l1-Ms for small sample sizes. However, no evident differences are observed among the six algorithms with large sample sizes.
We present the synchronization of two chaotic systems. These systems consist of solvable chaotic oscillator circuits operating at 10kHz with similar parameters. Although many chaotic systems have ...been synchronized, few instances of synchronized solvable chaos have been reported in hardware. Here, we use the analytical solution of solvable chaos to quantitatively measure the effect of coupling on the synchronized chaotic systems. The resulting oscillators are characterized by their time-series, return maps, phase portraits and finally by their closed-form analytical solutions. We subsequently synchronize these systems via bidirectional resistive coupling. Synchronization of these types of systems enables phase synchronization applications and clock recovery in popular ranging and secure communication schemes such as bistatic radar, chaotic mask and chaos shift keying (CSK).
The firefly algorithm is a member of the swarm intelligence family of algorithms, which have recently showed impressive performances in solving optimization problems. The firefly algorithm, in ...particular, is applied for solving continuous and discrete optimization problems. In order to tackle different optimization problems efficiently and fast, many variants of the firefly algorithm have recently been developed. Very promising firefly versions use also chaotic maps in order to improve the randomness when generating new solutions and thereby increasing the diversity of the population. The aim of this review is to present a concise but comprehensive overview of firefly algorithms that are enhanced with chaotic maps, to describe in detail the advantages and pitfalls of the many different chaotic maps, as well as to outline promising avenues and open problems for future research.
•The Melnikov method is used to predict chaotic motions of asymmetric TEHs.•The critical threshold curves of the Melnikov function for TEHs are obtained.•The output responses of different nonlinear ...energy harvesters are compared.
Ambient vibration conditions greatly influence the response of nonlinear energy harvesters. Recently, simulations and experiments have verified that tristable energy harvesters have excellent energy harvesting performance and complex nonlinear characteristics, which are important in broadening their effective operating frequency range. The response mechanism of the asymmetric tristable energy harvester is more complex than its symmetric counterpart. Owing to the complexities of the former, streamlined design methodologies and methods remain scarce. To facilitate future innovation and research on asymmetric tristable energy harvesters, this paper examines their nonlinear characteristics and energy harvesting performance. The Melnikov method is employed to predict the occurrence of chaotic motion, which is verified by numerical simulations. The chaotic dynamical system theory provides a simplified analytical framework that provides deeper insights into the performance of the asymmetric tristable energy harvester. Compared with its symmetric counterpart, the asymmetric tristable energy harvester can more easily jump into the interwell motion and output the higher voltage under low-level excitations.
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