4/1/2023 0 Comments Entropy journalIn the paper “New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields”, Jiri Petrzela and Roman Sotner described the evolution of a new active element that is able to significantly simplify the design process of a lumped chaotic oscillator. In the encryption scheme, the new chaotic system was used as the measurement matrix for compressed sensing, and Arnold was used for scrambling the image further. The performance analysis showed that the chaotic system has two positive Lyapunov exponents and high complexity. In the paper “Image Encryption Scheme with Compressed Sensing Based on New Three-Dimensional Chaotic System”, Yaqin Xie, Jiayin Yu, Shiyu Guo, Qun Ding, and Erfu Wang proposed a new three-dimensional chaotic system for image encryption. Therefore, the chaotic system was discretized and implemented by Digital signal processing (DSP) technology, and the National Institute of Standards and Technology (NIST) and approximate entropy analyses were computed. They observed coexisting attractors and multistability that could be used to obtain a pseudorandom sequence generator for digital encryption systems. In the paper “Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit”, Yixuan Song, Fang Yuan, and Yuxia Li presented a new absolute voltage-controlled memristor and described the construction of a simple three-order Wien-bridge chaotic circuit without inductor on the basis of the proposed memristor. They found that the polynomial chaotic maps satisfy the Li–Yorke definition of chaos, and through the existence and stability analysis of fixed points, they proved that such class quadratic polynomial maps cannot have hidden chaotic attractors. In the paper “A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis”, Chuanfu Wang and Qun Ding studied a class of quadratic polynomial chaotic maps. By calculating the entropy, energy, and homogeneity of attractors’ images and basins of attraction, they showed an increase in the complexity of attractors when changing the bifurcation parameters. Alsaadi, Tasawar Hayat, and Viet-Thanh Pham proposed a modified nonlinear oscillator which has an infinite number of coexisting torus attractors, strange attractors, and limit cycle attractors. In the paper “A Giga-Stable Oscillator with Hidden and Self-Excited Attractors: A Megastable Oscillator Forced by His Twin”, Thoai Phu Vo, Yeganeh Shaverdi, Abdul Jalil M. The overall purpose of the second volume of this Special Issue is to gather the latest scientific advances on topics of dynamics, entropy, fractional-order calculus, and applications in complex systems with hidden attractors and self-excited attractors. There is evidence that the mentioned dynamics play a vital role in various fields ranging from living systems (economics, neural networks, neural computing, neurostimulation, and so on) to nonliving systems (control theory, circuits, memristors, encryption, random number generators, etc.). By introducing a fractional order for the derivatives of dynamical systems, the memory properties can be also considered. Additionally, in complex systems with hidden and self-excited attractors, several behaviors, such as multistability, extreme multistability, coexisting attractors, and transient chaos, can be observed as functions of the system’s parameters and initial conditions. Nonlinear complexity measures may include fractal dimensions, correlation dimension, Lyapunov exponents, K-S entropy, approximate entropy, permutation entropy, and multiscale entropy. In this framework, it is essential to study the complexity of nonlinear systems. Hence, the paradigm of deterministic chaos for complex nonlinear systems is becoming increasingly popular for its attractive concept and successful real-world applications. While a self-excited attractor presents a basin of attraction associated with an unstable equilibrium, a hidden attractor has a basin of attraction that does not intersect with small neighborhoods of the unstable equilibrium. According to the pioneering work of Leonov and Kuznetsov, the attractors in complex systems can be classified as self-excited and hidden attractors.
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