Article
Materials Science, Multidisciplinary
Chunyi Dong, Karthikeyan Rajagopal, Shaobo He, Sajad Jafari, Kehui Sun
Summary: This paper presents a chaotification method based on the internal perturbation model (IPM) which can be applied to various maps, with further research on integer-order and fractional-order Sine-series maps. IPM method expands parameter space and complexity while maintaining the system's topological structure, validating its effectiveness in digital signal processing.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Mechanical
Andre Gusso, Sebastian Ujevic, Ricardo L. Viana
Summary: Numerical demonstration shows that two-frequency excitation can effectively induce chaos in the Duffing oscillator with single- and double-well potentials, with chaos being robust in the latter case. The robust chaos is characterized by the existence of a single chaotic attractor unaffected by parameter changes, necessary for practical applications to prevent chaos destruction by fabrication tolerances, external influences, and aging.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics
Lazaros Moysis, Ioannis Kafetzis, Murilo S. Baptista, Christos Volos
Summary: This paper proposes a chaotification technique that enhances the complexity of one-dimensional maps using the remainder operator. The technique produces maps with higher Lyapunov exponents and stable chaotic behaviors. Additionally, the technique demonstrates advantages in the problem of pseudo-random bit generation.
Article
Multidisciplinary Sciences
Marcin Lawnik, Lazaros Moysis, Christos Volos
Summary: In this work, a family of piecewise chaotic maps is proposed, which is parameterized by nonlinear functions used for each piece of the mapping. The generated maps have no equilibria and exhibit chaotic behavior due to a constraint applied to the shape of each piece. This family belongs to the category of systems with hidden attractors. Examples of chaotic maps are provided, showing fractal-like, symmetrical patterns at the transition between chaotic and non-chaotic behavior. Furthermore, the proposed maps are successfully applied to a pseudorandom bit generator.
Article
Mathematics
Tareq Hamadneh, Abderrahmane Abbes, Hassan Al-Tarawneh, Gharib Mousa Gharib, Wael Mahmoud Mohammad Salameh, Maha S. Al Soudi, Adel Ouannas
Summary: In this study, a 2D sine map is expanded to a 3D fractional-order sine-based memristor map by adding a discrete memristor. Through various numerical techniques, the nonlinear dynamic behaviors of the map under commensurate and incommensurate orders are extensively explored, and its sensitivity to fractional-order parameters is emphasized, leading to the emergence of distinct and diverse dynamic patterns. The complexity of the map is quantitatively measured using the sample entropy method and C0 complexity, and the presence of chaos is validated using the 0-1 test. MATLAB simulations are executed to confirm the obtained results.
Article
Physics, Multidisciplinary
Xintong Han, Xiuguo Bi, Bo Sun, Lujie Ren, Li Xiong
Summary: This paper introduces the application of discrete memristor models in discrete maps, and investigates the dynamical characteristics and multistability of the memristor cosine map.
FRONTIERS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Lazaros Moysis, Marcin Lawnik, Ioannis P. P. Antoniades, Ioannis Kafetzis, Murilo S. S. Baptista, Christos Volos
Summary: In this work, a chaotification technique is proposed to increase the complexity of chaotic maps by combining the most- and least-significant digits. The resulting map achieves a higher Lyapunov exponent value through parameter tuning. The transformed chaotic map is utilized for the encryption of B-spline curves and patches, resulting in visually unrecognizable ciphertext and strong performance on statistical tests.
Article
Multidisciplinary Sciences
Xianming Wu, Shaobo He, Weijie Tan, Huihai Wang
Summary: This paper proposes a new jerk system based on the proposed generalized memristor and investigates its complex dynamics through experiments and numerical simulations. The principles regarding whether nonlinear systems with a memristor function can be realized using a memristor device are also discussed.
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
Physics, Multidisciplinary
Chenyang Wu, Kehui Sun, Yan Xiao
Summary: This paper proposes a chaotification method to enhance the non-linear performance of one-dimensional chaotic maps, constructing a multi-cavity discrete chaotic map to achieve this. The method demonstrates better performance in terms of dynamical behavior, complexity, and Lyapunov exponent, as well as resistance to parameter identification.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Physics, Multidisciplinary
Abderrahmane Abbes, Adel Ouannas, Nabil Shawagfeh
Summary: This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order and investigates its dynamical behavior analytically and numerically. The results show that the system exhibits chaotic behavior, which is verified through bifurcation diagrams, phase attractors, the maximum Lyapunov exponent, the 0-1 test, approximation entropy (ApEn), and C (0) complexity analyses. Finally, numerical simulations are used to present the main findings of this study.
Review
Chemistry, Multidisciplinary
Jianbo Gao, Bo Xu
Summary: This article proposes the synergistic use of machine learning and multiscale approaches to study complex systems and emergence. The multiscale approaches are helpful in identifying key parameters for system evolution and designing more accurate unsupervised machine learning schemes.
APPLIED SCIENCES-BASEL
(2021)
Article
Automation & Control Systems
Kianoush Falahkheirkhah, Kevin Yeh, Shachi Mittal, Luke Pfister, Rohit Bhargava
Summary: This study introduces a deep learning framework for extracting and processing data in infrared imaging. Utilizing convolutional neural networks and generative adversarial networks, the framework facilitates data classification, reconstruction, and acceleration of data acquisition. The research also explores new methods to enhance data quality and speed.
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
(2021)
Article
Mathematics, Interdisciplinary Applications
Xiaohua Ren, Changcheng Xiang, Yi Yang
Summary: This paper investigates the effects of random perturbations on interacting populations and proposes a discrete-time model with biological control. The results show that random perturbations change the number of blurred orbits of the system, enhancing its stability.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics
Zai-Yin He, Abderrahmane Abbes, Hadi Jahanshahi, Naif D. Alotaibi, Ye Wang
Summary: This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination and examines its dynamical behavior analytically and numerically. It is verified that the introduced fractional discrete SIR epidemic model with both commensurate and incommensurate fractional orders exhibits chaotic behavior. The discrete fractional model displays more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders.
Article
Physics, Multidisciplinary
Janarthanan Ramadoss, Hayder Natiq, Fahimeh Nazarimehr, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper proposes the behavior of a 1D chaotic map that includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map generates a shift and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term results in stable fixed points in some parameter intervals by increasing the bifurcation parameter. The proposed system, known as multistable, achieves multiple steady states in some intervals of the parameter, and the multistability dynamics are investigated using cobweb diagrams that reveal an interesting asymmetry in repeating parts of the bifurcation diagram.
Article
Computer Science, Information Systems
Gayathri Vivekanandhan, Hayder Natiq, Yaser Merrikhi, Karthikeyan Rajagopal, Sajad Jafari
Summary: In this paper, a memristor is added to the two-dimensional neural model Chialvo to consider the effects of electromagnetic induction. The dynamics of the system are analyzed by obtaining bifurcation diagrams and Lyapunov spectra. The study shows that the magnetic strength and injected current are the most effective parameters on the dynamics. The memristive Chialvo can exhibit different neural behaviors and has coexisting attractors, similar to the primary Chialvo model. Furthermore, it is found that electrical coupling is essential for synchronization in the network of memristive Chialvo, while chemical coupling alone does not lead to synchronization.
Article
Mathematics, Applied
Fatemeh Parastesh, Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper proposes an optimization algorithm based on the eigenvalues of the connectivity matrix to construct a network with optimal synchronization. The proposed algorithm shows better synchronization ability compared to random link addition and a method based on eigenvector centrality. It also performs well in preserving synchronization in scale-free and small-world networks with the same number of nodes and links. Additionally, the algorithm is effective for link reduction while maintaining synchronization.
Article
Computer Science, Artificial Intelligence
Hayder Natiq, Animesh Roy, Santo Banerjee, A. P. Misra, N. A. A. Fataf
Summary: This paper investigates and analyzes the dynamics of the two-dimensional Duffing map and observes multistability behavior numerically. In order to address the undesired coexistence of chaotic and periodic attractors in chaos-based cryptography, a Sine-Cosine chaotification technique is designed and implemented to enhance chaos in the multi-stable regions. Additionally, a new image encryption algorithm is proposed to evaluate the performance of the generalized Duffing map in cryptography applications, showing that the proposed algorithm can effectively encrypt and decrypt several image types with a high level of security.
Article
Mathematics, Interdisciplinary Applications
Atefeh Ahmadi, Sriram Parthasarathy, Hayder Natiq, Sajad Jafari, Igor Franovic, Karthikeyan Rajagopal
Summary: This paper introduces the first three-dimensional non-autonomous chaotic system that displays both megastability and extreme multistability, jointly called mega-extreme multistability. Different types of coexisting attractors are characterized by phase portraits, first return maps, bifurcation diagrams, Lyapunov spectra, Kaplan-Yorke dimension, connecting curves, and basins of attraction. The dissipative nature of the system is demonstrated, and the feasibility and applicability of the model are shown through analog circuit simulation.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Ahmed M. Ali Ali, Sridevi Sriram, Hayder Natiq, Atefeh Ahmadi, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper presents a novel one-dimensional trigonometric chaotic map that is multi-stable. The stability conditions and behaviors of the map are analyzed and validated, and the influence of parameter variations on the map's outputs is examined through bifurcation diagrams and Lyapunov exponent spectra.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Sriram Parthasarathy, Fatemeh Parastesh, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari
Summary: The paper investigates the changes in dynamics of the Rulkov model by considering autaptic current, showing that autapse parameters greatly affect the firing patterns and that inhibitory autapse leads to enhanced firing activity. In addition, the synchronous dynamics of coupled Rulkov maps in the presence of autapse are studied, revealing that electrical autapse enhances synchronization in small time delays, while chemical autapse achieves synchronization regardless of time delay, although increasing the time delay reduces the synchronization region.
Article
Physics, Multidisciplinary
Rending Lu, Prasina Alexander, Hayder Natiq, Anitha Karthikeyan, Sajad Jafari, Jiri Petrzela
Summary: This study investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. Bifurcation diagrams reveal the presence of coexisting attractors, and the synchronization behavior of the system is examined for various derivative orders. Theoretical findings are validated through the implementation of integer-order and fractional-order electronic circuits. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.
Article
Physics, Multidisciplinary
Dorsa Nezhad Hajian, Gayathri Vivekanandhan, Hayder Natiq, Fatemeh Parastesh, Karthikeyan Rajagopal, Safari Jafari
Summary: This paper investigates the complete synchronizability of coupled periodically forced chaotic systems using the master stability function method. Three classic chaotic systems are employed for this study, and numerical simulations supporting the findings are reported. The results suggest that chaotic forced systems tend to synchronize at weaker couplings than the autonomous versions with increased stimulation, while high-frequency stimulation is completely ineffective. The required forcing amplitude also depends on the system's attractor size.
Article
Physics, Multidisciplinary
Gayathri Vivekanandhan, Hayder Natiq, Aboozar Ghaffari, Atiyeh Bayani, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper presents a chaotic jerk oscillator with a heart-shaped attractor and the coexistence of chaotic and periodic attractors. The analysis of bifurcation diagram, Lyapunov exponent, and basin of attraction confirms the chaotic and periodic properties of the oscillator.
Article
Physics, Multidisciplinary
Balamurali Ramakrishnan, Hayder Natiq, Ahmed M. Ali Ali, Karthikeyan Rajagopal, Fahimeh Nazarimehr, Sajad Jafari
Summary: This paper presents a mathematical model for examining the hemostatic behaviors of neural activity and extracellular matrix (ECM) molecules. The dynamic behaviors of the proposed model are investigated using tools such as Lyapunov exponents and bifurcation diagrams. The coexistence of periodic and chaotic dynamics in ECM is demonstrated, which is believed to be distinct modulation modes of neuronal circuits. Additionally, the synchronization characteristics of the coupled systems are examined using the master stability function, showing that certain coupling configurations can synchronize the models. This research is significant for neurologists to understand brain rhythms and their roles.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematical & Computational Biology
Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Ondrej Krejcar, Hamidreza Namazi
Summary: Investigating the effect of changes in neuronal connectivity on the brain's behavior is a crucial topic in neuroscience. Complex network theory provides a powerful tool to study these changes. This paper focuses on the effect of asymmetry coupling changes on the behaviors of a multi-layer neuronal network.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematical & Computational Biology
Gayathri Vivekanandhan, Hamid Reza Abdolmohammadi, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Hamidreza Namazi
Summary: This paper introduces the fractional order discrete Rulkov neuron map and analyzes its dynamics and synchronization ability. The results show that increasing the order of the fractional order decreases the stable areas of the system, and the fractional order systems cannot achieve complete synchronization.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Applied
Gokulakrishnan Sriram, Fatemeh Parastesh, Hayder Natiq, Karthikeyan Rajagopal, Riccardo Meucci, Sajad Jafari
Summary: This paper investigates the effects of a switching parameter on the dynamics of a multistable laser model. It is found that the attractor of a fast blinking system may differ from the average attractor.
Article
Physics, Multidisciplinary
Gayathri Vivekanandhan, Mahtab Mehrabbeik, Hayder Natiq, Boshra Hatef, Yaser Merrikhi, Sajad Jafari
Summary: This paper investigates the collective behaviors of a one-dimensional piecewise nonlinear map-based neuronal model in complex networks. Different firing patterns, including synchronous firing, cluster synchronization, imperfect synchronization, chimera, and solitary state, are observed under different conditions.
PRAMANA-JOURNAL OF PHYSICS
(2023)
