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Article
Multidisciplinary Sciences
Haitao Qiu et al.
Summary: In this paper, a novel three-dimensional chaotic system with strange characteristic is introduced by applying a construction method of a 3D chaotic circuit. The system exhibits multiple equilibria and abundant coexisting attractors. A mathematical model is developed and stability analyses for equilibrium points are conducted, yielding significant results of period-doubling bifurcation patterns confirmed by phase plane plots and Lyapunov exponent spectra. By varying the initial value and a unique controlled parameter, the double-scroll chaotic attractor is broken up into a pair of symmetric singular attractors. Furthermore, the local basins of attraction are investigated with respect to the initial condition. The circuit synthesis results generated by Multisim simulation tool validate the self-excitation characteristics of this system. Finally, the feedback control technique is utilized to study difference synchronization of this system, and the main conclusions confirm the validity and reliability of difference synchronization.
SCIENTIFIC REPORTS
(2023)
Article
Multidisciplinary Sciences
Gamal M. Mahmoud et al.
Summary: In this paper, a new type of synchronization called compound-combination synchronization (CCS) for fractional order hyperchaotic models with different orders is introduced. The tracking control method is used to calculate the analytical controllers that achieve the proposed synchronization and a theorem is described and proved. The hyperchaotic complex Lu, Chen, and Lorenz models with complex periodic forcing are also introduced, and the symmetry property is found in these models. The numerical simulations show good agreement with the analytical results. The proposed synchronization scheme is considered a generalization of many types in the literature and can be applied in various similar studies.
Article
Mathematics
Fei Yu et al.
Summary: In this paper, a simple seven-term 4D hyperchaotic system based on the classical Sprott-C 3D chaotic system is presented. The system is inspired by a previous study on a simple 4D hyperchaotic system. The paper discusses the limitations of the previous system and proposes an improved 5D memristive hyperchaotic system with hidden attractors. The properties of the new system are analyzed and hardware circuits are realized and verified through experiments.
Article
Mathematics
Xiaoyuan Wang et al.
Summary: This paper proposes a new color image encryption algorithm based on a hyper-chaotic system constructed by a tri-valued memristor. The encryption process is based on the structure of permutation-diffusion, and the transmission of key information is realized through hyper-chaotic synchronization technology. The results show that the scheme has excellent encryption performance and can resist a variety of attacks, making it suitable for secure image communication fields.
Article
Physics, Multidisciplinary
Chengqiang Wang et al.
Summary: Chaotic nonlinear dynamical systems are extensively used to accurately track the complex fluctuations of real-world financial markets. In this study, we focus on a financial system described by semi-linear parabolic partial differential equations. We prove the global well-posedness of the concerned partial differential equations using Galerkin's method and a priori inequalities. We also design controls and demonstrate the drive-response fixed-time synchronization of our financial system. Numerical simulations are performed to validate the theoretical results. Overall, we give a rating of 8 out of 10 for the importance of this article.
Article
Engineering, Mechanical
Ertong Wang et al.
Summary: This paper proposes a simple hyperchaotic system with only two nonlinear terms and discusses its complex properties. The results show that the system exhibits transient chaos and attractor coexistence, as well as controllable spike numbers and symmetric bursting phenomena.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Kun Li et al.
Summary: In this paper, a memristor-based hyper-chaotic Bao-like system is successfully constructed based on a three-dimensional Bao system, and a simulated equivalent circuit is designed to verify the chaotic behaviors. A control method called periodically intermittent control with variable control width is proposed, featuring a variable and monotonically decreasing control width sequence, which can effectively stabilize most existing nonlinear systems. Moreover, the memristor-based hyper-chaotic Bao-like system is controlled by combining the proposed method with the Lyapunov stability principle. The proposed method can effectively control and stabilize not only the proposed hyper-chaotic system but also the Chua's oscillator.
Article
Mathematics, Interdisciplinary Applications
Mohammed Almuzaini et al.
Summary: The study proposes a new chaotic system with a cubic non-linear term and investigates various characteristics of the system such as equilibria, stability, invariance, dissipation, Lyapunov dimension, and Lyapunov exponents. The electronic circuit and signal flow graph are implemented to demonstrate the applicability of the chaotic system. The study also focuses on achieving complete synchronization between two similar novel chaotic systems and applying it in secure communication using Lyapunov stability theorem.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Ke-Yong Shao et al.
Summary: In this study, a sliding mode control method based on fixed-time sliding mode surface was proposed for the synchronization of uncertain fractional-order hyperchaotic systems. A novel self-evolving non-singleton-interval type-2 probabilistic fuzzy neural network (SENSIT2PFNN) was also proposed to estimate the uncertain dynamics of the system. An adaptive compensator was designed to eliminate the influences of random uncertainty and fuzzy uncertainty, yielding an asymptotically stable controlled system. Furthermore, an adaptive law was introduced to optimize the consequence parameters of SENSIT2PFNN. The membership layer and rule base of SENSIT2PFNN were optimized using self-evolving algorithm and whale optimization algorithm, respectively. Simulation results verified the effectiveness of the proposed methods for the synchronization of uncertain fractional-order hyperchaotic systems.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
Gang Yang et al.
Summary: A novel, simple, four-dimensional hyperchaotic memristor circuit is designed, which exhibits rich attractor evolution phenomenon and has large-scale parameter permission. The circuit's spectral entropy complexity is analyzed, confirming significant amount of dynamical behavior. Multiple coexisting attractors are found under symmetric initial conditions, and attractor basin results further confirm the coexisting attractor behavior and multiple stability. A simple memristor chaotic circuit is then designed using FPGA technology, which shows the same phase trajectory as the numerical calculation results. The hyperchaotic memristor circuit has potential applications in secure communication, intelligent control, and memory storage.
Article
Engineering, Electrical & Electronic
Nasreen Khan et al.
Summary: The paper introduces a new 5D fractional-order hyperchaotic memristive system and demonstrates its complex characteristic dynamics as well as its application in the digital world, highlighting its significance.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Fatemeh Aliabadi et al.
Summary: This paper proposes an adaptive controller for chaos synchronization using quantum neural networks. The main purpose is to design a communication system for transmission of information securely. The proposed method utilizes quantum neural networks to estimate uncertainties in the receiver and improve the accuracy of synchronization and recovering the message signal for secure communication.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Engineering, Mechanical
Zefeng Zhang et al.
Summary: In this paper, a new five-dimensional hyperchaotic system is proposed based on Euler equation and energy analysis. The conservative and chaotic properties of the system are verified, and the multistability phenomenon and transient transition behavior are analyzed.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
A. A-H Shoreh et al.
Summary: This report investigates an adaptive synchronization for complex hyperchaotic models with unknown parameters, proposing a new algorithm for achieving this type of synchronization. Special control based on adaptive laws of parameters is constructed analytically for secure communications, with simulated results validating the algorithm's accuracy. A strategy for secure communication is proposed, splitting the message and inserting bits of information signal into modulation parameters and transmitter system's states to enhance security.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Tsafack Nestor et al.
Summary: In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. The dynamics of the system are investigated, and a novel image encryption scheme based on the hyperchaotic behavior is proposed. The performance analysis shows that the proposed cryptosystem outperforms recently published algorithms.
Article
Mathematics
Khalid A. Alattas et al.
Summary: This study proposes an integral-type sliding mode control method to synchronize a category of hyper-chaotic systems, guaranteeing fast synchronization in the presence of uncertainty. The effectiveness of the new control scheme is demonstrated using a new six-dimensional hyper-chaotic system.
Article
Computer Science, Artificial Intelligence
Xueyan Yang et al.
Summary: This paper introduces a method for finite-time lag synchronization of uncertain complex networks involving impulsive disturbance effects. By designing different controllers, the synchronization of systems can be guaranteed, and it is found that the synchronization time depends on the initial values and impulse sequences. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Mathematics, Applied
Junhong Li et al.
Summary: In this paper, a new hyperchaotic Hamiltonian system is formulated and the existence of multiple equilibrium points in the system is demonstrated. The characteristics of equilibrium points, Lyapunov exponents and Poincare sections are studied. Additionally, the complex dynamical behaviors of the system under holonomic and nonholonomic constraints are investigated. The results show that the hyperchaotic system can be generated by introducing constraints and controlled through linear feedback control.
Article
Computer Science, Information Systems
Chih-Hsueh Lin et al.
Summary: In this paper, a novel chaos-based cryptosystem is proposed to ensure the communication security of video/audio streaming in the network environment. The system utilizes synchronization controllers and dynamic key generators to achieve synchronized and dynamic encryption process. Through testing and comparisons, the quality of the random sequences generated by the system is proven to be good.
MULTIMEDIA SYSTEMS
(2022)
Article
Physics, Multidisciplinary
Xiurong Yao et al.
Summary: This article introduces a memristor-based sixth-order chaotic circuit and designs an adaptive terminal sliding-mode control law for chaotic systems. Simulation examples demonstrate the significance and superiority of the control scheme, achieving positive results in the field of image encryption.
FRONTIERS IN PHYSICS
(2022)
Article
Physics, Multidisciplinary
Ya Wang et al.
Summary: In this paper, a new 5-D hyperchaotic system was constructed with high order nonlinear terms, along with a multivariable nonlinear feedback synchronous controller proposed for synchronization of high order complex hyperchaotic systems. Experimental results demonstrated rapid convergence of error signal to 0 under the effect of the controller, laying the foundation for synchronization of high order complex chaotic systems.
Article
Computer Science, Information Systems
Tien-Loc Le et al.
Summary: This study introduces a novel fuzzy neural network controller that can effectively synchronize complex systems and enhance the system's response to uncertainty. System stability is ensured through adaptation laws and stability analysis, and the performance of the controller is validated through numerical simulations.
Article
Mathematics, Interdisciplinary Applications
Chengwei Dong et al.
Summary: This paper presents a four-dimensional (4D) novel hyperchaotic system and investigates its complex dynamical behaviors, including hidden chaotic and hyperchaotic attractors, as well as five types of coexisting attractors. The numerical verification is performed by analyzing phase diagrams, Poincare maps, the Lyapunov exponent spectrum, and its bifurcation diagram. The short unstable cycles in the hyperchaotic system are systematically explored via the variational method, and the symbol codings of the cycles with four letters are realized based on the topological properties. The bifurcations of the cycles are explored through a homotopy evolution approach, and the novel 4D system is implemented by an analog electronic circuit, which is consistent with the numerical simulation results.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Information Systems
A. N. H. T. U. A. N. VO et al.
Summary: This paper investigates complex modified function projective lag synchronization with fixed-time stability guarantees for hyperchaotic systems. The proposed method ensures the synchronization and desired performance of complex hyperchaotic systems within a bounded time, without requiring the initial conditions from the systems. The fixed-time stability guarantees are achieved using the Lyapunov principle, and the settling time is calculated by solving differential equations.
Article
Mathematics, Interdisciplinary Applications
Qijia Yao
Summary: This paper proposes a novel fixed-time adaptive sliding mode control scheme for the synchronization of second-order chaotic systems with system uncertainties and external disturbances. The controller is able to guarantee that synchronization tracking errors converge to an arbitrarily small neighborhood of zero in fixed time even in the presence of lumped disturbances, which demonstrates excellent performance in the same conditions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Artificial Intelligence
Jianhua Dai et al.
Summary: This paper presents a noise-suppression zeroing neural network (NSZNN) to effectively resist time-varying external disturbances in chaotic systems, demonstrating consistent robustness for both bounded and unbounded noises. The NSZNN shows better synchronization control performance under bounded and unbounded noises compared with existing zeroing neural network models, as confirmed by theoretical and numerical analysis.
Article
Engineering, Multidisciplinary
Emad E. Mahmoud et al.
Summary: The study investigates the control and synchronization of a novel five-dimensional hidden attractors hyperchaotic system, proposing an effective control method and focusing on stability theory. Numerical simulations demonstrate successful results in control and synchronization.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Guessas Laarem
Summary: This research article presents the discovery of a new twelve term hyper-chaotic system and its stabilization and synchronization control methods using genetically optimized controllers and fractional order sliding mode controllers.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Wei Chen
Summary: This study utilizes highway traffic flow data, community detection, and core-periphery profile algorithms to identify 21 megaregions in China and delineate their spatial boundaries. There are spatial differences in the number, size, and density of megaregions in different regions of China.
Article
Optics
B. Wang et al.
Summary: This paper addresses the problem of image encryption using a chaotic system with time delay. A new time delay chaotic system is proposed with different dynamical behaviors, and a novel approach is designed based on the system's time delay for image encryption. Experimental results show that the proposed method has good effectiveness and higher security.
Article
Mathematics, Interdisciplinary Applications
Pei-Ying Xiong et al.
Summary: A vast amount of research has been devoted to chaotic systems due to their diverse applications. This study investigates a multi-stable fractional-order chaotic system and proposes a new control method using a neural network for synchronization and disturbance rejection. The results demonstrate the effectiveness and disturbance rejection capability of the proposed method.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Automation & Control Systems
Kevin Herman Muraro Guiarte et al.
Summary: This paper introduces a unified identification algorithm for uncertain systems online, ensuring boundedness of errors and convergence of state estimation error. The peculiarity lies in adjusting identification transient using parameters not related to residual state error. Two examples validate the theoretical results, demonstrating relevance for online weld geometry prediction.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2021)
Article
Engineering, Mechanical
Chenguang Ma et al.
Summary: This paper presents a new four-dimensional dissipative chaotic system capable of producing multiple asymmetric attractors, with analysis on its dynamical behavior. The system exhibits asymmetric multistability in the basin of attraction, and different types of asymmetric coexisting attractors are observed with changes in bifurcation parameters. The spectral entropy complexity chaotic diagrams are used to observe changes in sequence complexity as bifurcation parameters change simultaneously.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Multidisciplinary
Adel Ouannas et al.
Summary: This paper proposes a new secure communications approach by combining chaotic modulation, recursive encryption, and chaotic masking into one scheme. The objective is achieved by synchronizing two hyperchaotic Lorenz systems with encrypted states using backstepping technique. A novel theorem is proved to ensure message recovery at the receiver side through synchronization of the Lorenz systems. Numerical simulations demonstrate the effectiveness of the chaos-based encryption scheme.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematical & Computational Biology
Ahmed S. Al-Obeidi et al.
Summary: A novel 7D hyperchaotic model is constructed from the 6D Lorenz model using nonlinear feedback control technique, with only an unstable origin point. The model is categorized as having self-excited attractors and exhibits dynamical behaviors such as chaotic and hyperchaotic. The paper also presents hybrid synchronization for the novel model via Lyapunov stability theory.
COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE
(2021)
Review
Mathematics, Interdisciplinary Applications
El Abed Assali
Summary: This paper investigates predefined-time synchronization analysis for two chaotic systems with different dimensions. A new control protocol is proposed based on predefined-time stability, and adaptive control is used to consider parameter uncertainties. The efficacy of the results is confirmed through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Jian-Jun He et al.
Summary: A novel four-dimensional chaotic system with three quadratic nonlinearities and only one unstable equilibrium is reported in this paper. The system exhibits periodic, quasi-periodic, and chaotic motions with the variation of parameters and generates symmetric coexisting attractors for different initial conditions. Additionally, the circuit implementation and impulsive synchronization control of the system are well investigated, yielding theoretical and numerical results.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Physics, Multidisciplinary
Hai-Yong Cao et al.
Summary: This paper introduces an interesting four-dimensional chaotic system with different equilibria and attractors, presenting stable, periodic and chaotic states as parameters change. The system exhibits period-doubling and Hopf bifurcations, along with hidden chaotic attractors and coexisting chaotic attractors. The electronic circuit implementation is provided to demonstrate the system's dynamical properties.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Physics, Multidisciplinary
Yazheng Wu et al.
Summary: A new 3D multi-scroll hidden attractor chaotic system is proposed in this paper, which has chaotic attractors with no equilibrium point and hidden attractors that can be obtained by varying a parameter. The system generates multi-scroll attractors through a piecewise linear function and has applications in communication encryption. Circuit experiments validate the feasibility of this system's different cases.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Automation & Control Systems
Ho Pham Huy Anh et al.
Summary: This paper introduces a novel advanced single-hidden layer neural extreme learning machine model with nonlinear parameters (ASHLN-ELM), in which hidden and output weighting values are updated simultaneously using adaptively robust rules based on Lyapunov stability principle. The proposed approach guarantees fast convergence and limits state-estimation residual errors to zero without the need for knowledge related to desired weighting values or required approximating error. The efficiency and robustness of the method are demonstrated using typical uncertain hyper-chaotic benchmark systems.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Engineering, Multidisciplinary
M. M. El-Dessoky et al.
Summary: This investigation focuses on applying feedback control method to control the behavior of a new hyperchaotic system, demonstrating the stability of the controlled system and achieving results for adaptive modified function projective synchronization. Numerical results justify the importance of the considered method in practice.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Computer Science, Information Systems
Saleh Mobayen et al.
Summary: This study introduces a family of nine new chameleon chaotic systems, identifies different types of hidden attractors and self-excited attractors, and explores methods for controlling these systems under uncertainties and disturbances.
Article
Computer Science, Information Systems
Rongwei Guo et al.
Summary: This paper investigates partial anti-synchronization in chaotic and hyper-chaotic systems, proving the existence of partial anti-synchronization in chaotic systems and deriving solutions using systematic methods. Physical controllers are designed and numerical simulations are used to verify the theoretical results.
Article
Computer Science, Information Systems
Kevin Herman Muraro Gularte et al.
Summary: This paper proposes a scheme for secure telecommunication based on the projective synchronization of hyperchaotic systems. The design of the synchronizer considers the presence of disturbances to increase the robustness of the method, requiring only two control inputs to synchronize the master and slave systems. The proposed approach ensures the finite-time convergence of the synchronization error to a small neighborhood of the origin, even in the presence of disturbances in all states, simplifying the control structure and applications.
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AM Chen et al.
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(2006)
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(2005)
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JH Lu et al.
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(2002)
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JC Sprott
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