Article
Physics, Multidisciplinary
Kei Inoue
Summary: The Lyapunov exponent is a commonly used measure for quantifying chaos in a dynamical system, but its computation requires specific information. The entropic chaos degree quantifies chaos in a dynamical system as an information quantity and can be computed directly for any time series, regardless of knowledge about the dynamical system. A recent study introduced the extended entropic chaos degree, which achieved the same value as the sum of Lyapunov exponents under typical chaotic conditions. An improved computation formula for the extended entropic chaos degree was proposed to obtain accurate numerical results for multidimensional chaotic maps. This study demonstrates that all Lyapunov exponents of a chaotic map can be estimated to compute the extended entropic chaos degree and proposes a computational algorithm for it, which was applied to one and two-dimensional chaotic maps. The results suggest that the extended entropic chaos degree may serve as a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.
Article
Physics, Multidisciplinary
Kei Inoue
Summary: The paper discusses the application of Lyapunov exponent and entropic chaos degree in quantifying chaos in dynamical systems, with a focus on reducing the difference between the two measures. It also presents an extension of the improved entropic chaos degree for multi-dimensional chaotic maps and proposes an improved calculation formula for obtaining suitable numerical computation results for two-dimensional chaotic maps.
Article
Mathematics, Applied
Kei Inoue, Tomoyuki Mao, Hidetoshi Okutomi, Ken Umeno
Summary: The Lyapunov exponent is used to quantify the chaos of a dynamical system, while entropic chaos degree is introduced in information dynamics to measure the strength of chaos. Both can be used to compute the chaos degree of a dynamical system. This paper attempts to extend the concept of entropic chaos degree in Euclidean space to enhance the measurement capability of chaos strength in dynamical systems, showing several relations with the Lyapunov exponent.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Kei Inoue, Kazuki Tani
Summary: This paper introduces a quantification method for chaos in traffic flow models. The extended entropic chaos degree can directly compute the chaos level of time series with lower computational complexity. Through empirical research, it is demonstrated that the extended chaos degree can be used to quantify chaos in traffic flow models.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Information Systems
Ranjeet Kumar Singh, Binod Kumar, Dilip Kumar Shaw, Danish Ali Khan
Summary: This paper presents a novel technique for employing a security mechanism in the transmission of digital contents over public network, using a multilevel image encryption/decryption algorithm based on quantum chaos map and sparse sampling. The results show the correctness of the algorithm in protecting multimedia contents.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2021)
Review
Physics, Multidisciplinary
M. S. Santhanam, Sanku Paul, J. Bharathi Kannan
Summary: The kicked rotor model is an important template for studying chaos and quantum chaos, with wide applications in nonlinear dynamics, quantum information, and other fields. Various problems can be addressed in the kicked rotor and its variants models, including complex system dynamics, resonant dynamics, and the relationship between quantum correlations and chaos.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2022)
Article
Physics, Multidisciplinary
Elena Kim, Robert Koirala
Summary: We investigate the norms of eigenfunctions of quantum cat maps that are l2-normalized. For maps with short quantum periods, we find a sequence of eigenfunctions with significantly large l∞ norms. For general eigenfunctions, we establish an upper bound on their l∞ norms. These results are similar to those previously obtained for compact Riemannian manifolds without conjugate points.
Article
Mathematics, Interdisciplinary Applications
Ahlem Gasri, Amina-Aicha Khennaoui, Adel Ouannas, Giuseppe Grassi, Apostolos Iatropoulos, Lazaros Moysis, Christos Volos
Summary: This study introduces a new fractional map with specific dynamic behaviors and properties, which is simpler than existing fractional maps. The dynamic and complexity of the map are investigated through numerical simulation, and it is applied to the encryption of signals.
Article
Mathematics
Amina-Aicha Khennaoui, Adel Ouannas, Shaher Momani, Othman Abdullah Almatroud, Mohammed Mossa Al-Sawalha, Salah Mahmoud Boulaaras, Viet-Thanh Pham
Summary: This study presents the implementation of a new chaotic fractional memristor map with hidden attractors. The system dynamics were analyzed with different fractional orders, revealing rich dynamical behavior.
Article
Mathematics, Interdisciplinary Applications
Wanting Zhu, Kehui Sun, Shaobo He, Huihai Wang, Wenhao Liu
Summary: In this paper, a new closed-loop multiple modulation coupling method is proposed to construct an enhanced chaotic system. A class of hyperchaotic maps is constructed based on the iterative chaotic map with infinite collapse (ICMIC) and Sinusoidal map. A new 3D-Hourglass chaotic map is also proposed. The dynamics analyses show that the proposed systems have good randomness, high permutation entropy complexity, and multiple coexistence attractor rings.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Sicong Liu, Yongxin Li, Xizhai Ge, Chunbiao Li, Yibo Zhao
Summary: A hyperchaotic map is constructed by combining exponential, cubic and sinusoidal nonlinearity, which provides two unipolar hyperchaotic sequences and a large area of hyperchaotic orbit. Based on this system, a fast video encryption algorithm using permutation-diffusion-permutation strategy is developed, which encrypts each frame image from the video stream in real time. The encryption process is accelerated by parallel encryption of frame images. Experimental results and security analysis confirm the algorithm's good security, robustness, and effectiveness.
Article
Automation & Control Systems
Longxiang Fu, Xianming Wu, Shaobo He, Huihai Wang, Kehui Sun
Summary: This article proposes an improved memristive Henon map by using the state variable difference as the input of a discrete memristor. The system exhibits rich dynamical behaviors as shown by bifurcation diagrams, Lyapunov exponent spectrums, and sample entropy complexity analysis results. In addition, analog circuits of the discrete memristor and memristive chaotic map are designed and validated through simulations and experiments, demonstrating the physical realizability of the discrete memristor and laying the foundation for its applications.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Chenyang Wu, Kehui Sun
Summary: In this paper, based on the mathematical expression of the rotating body in the cylindrical coordinate, the empty rotating-body chaotic model (ERCM) and the full rotating-body chaotic model (FRCM) are constructed. These two models have a pair of coexisting attractors with strictly symmetric phase space orbits, which can be used to construct multi-cavity chaotic systems with different attractors. The analysis of the cylindrical ERCM and FRCM demonstrates that these systems have wide chaotic range, large Lyapunov exponent, and high complexity. The DSP implementation of the proposed chaotic systems shows a promising application prospect in engineering.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Multidisciplinary Sciences
Kivanc Cetin, Ugur Tirnakli, Bruce M. Boghosian
Summary: Area-preserving maps exhibit chaotic and regular behavior in the available phase space. This paper explores the changes in the statistical mechanical framework of these maps as the control parameter changes. By studying a generalization of the standard map, the authors find that the probability distribution of the sum of system iterates follows a robust q-Gaussian distribution with a q value of approximately 1.935 for initial conditions chosen from nonergodic stability islands.
SCIENTIFIC REPORTS
(2022)
Article
Multidisciplinary Sciences
Marcin Lawnik, Marek Berezowski
Summary: The present article discusses a new dynamical system called M-map and its properties, as well as proposes a new image encryption algorithm and conducts corresponding analysis and comparison.
Article
Mathematics
L. Accardi, I. Ya. Aref'eva, I. V. Volovich
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
(2015)
Article
Mathematics, Applied
S. Iriyama, M. Ohya, I. V. Volovich
OPEN SYSTEMS & INFORMATION DYNAMICS
(2015)
Article
Physics, Multidisciplinary
A. S. Trushechkin, I. V. Volovich
Article
Physics, Multidisciplinary
Igor V. Volovich
Article
Mathematics, Applied
I. V. Volovich, S. V. Kozyrev
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
(2016)
Article
Physics, Multidisciplinary
Andrei Khrennikov, Borje Nilsson, Sven Nordebo, Igor Volovich
FOUNDATIONS OF PHYSICS
(2014)
Article
Mathematics
I. V. Volovich, A. S. Trushechkin
IZVESTIYA MATHEMATICS
(2012)
Article
Physics, Multidisciplinary
S. V. Kozyrev, I. V. Volovich
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2014)
Article
Mathematics, Applied
I. V. Volovich, V. Zh. Sakbaev
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
(2014)
Article
Mathematics, Applied
I. Ya. Aref'eva, I. V. Volovich
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
(2014)
Article
Physics, Multidisciplinary
I. Ya. Arefeva, I. V. Volovich
THEORETICAL AND MATHEMATICAL PHYSICS
(2013)
Article
Mathematics, Interdisciplinary Applications
B. Dragovich, S. V. Kozyrev, I. V. Volovich
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS
(2013)
Proceedings Paper
Physics, Applied
Andrei Khrennikov, Borje Nilsson, Sven Nordebo, Igor Volovich
QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS 6
(2012)
Proceedings Paper
Physics, Multidisciplinary
A. Khrennikov, B. Nilsson, S. Nordebo, I. V. Volovich
FOUNDATIONS OF PROBABILITY AND PHYSICS - 6
(2012)
Article
Mathematics, Interdisciplinary Applications
I. V. Volovich
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS
(2015)
