To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equati...To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz＇s, Chen＇s and Lu¨＇s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit.展开更多
Due to their biological interpretability,memristors are widely used to simulate synapses between artificial neural networks.As a type of neural network whose dynamic behavior can be explained,the coupling of resonant ...Due to their biological interpretability,memristors are widely used to simulate synapses between artificial neural networks.As a type of neural network whose dynamic behavior can be explained,the coupling of resonant tunneling diode-based cellular neural networks(RTD-CNNs)with memristors has rarely been reported in the literature.Therefore,this paper designs a coupled RTD-CNN model with memristors(RTD-MCNN),investigating and analyzing the dynamic behavior of the RTD-MCNN.Based on this model,a simple encryption scheme for the protection of digital images in police forensic applications is proposed.The results show that the RTD-MCNN can have two positive Lyapunov exponents,and its output is influenced by the initial values,exhibiting multistability.Furthermore,a set of amplitudes in its output sequence is affected by the internal parameters of the memristor,leading to nonlinear variations.Undoubtedly,the rich dynamic behaviors described above make the RTD-MCNN highly suitable for the design of chaos-based encryption schemes in the field of privacy protection.Encryption tests and security analyses validate the effectiveness of this scheme.展开更多
Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spher...Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.展开更多
This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fra...This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.展开更多
This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investi...This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.展开更多
Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of uns...Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as the origin of complexity of dynamical systems.展开更多
To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coup...To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.展开更多
Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled ...Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.展开更多
This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted （RCL-shunted） Josephson junctions （RCLSJJs） and a shunted resistor. Numerical simulations show that per...This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted （RCL-shunted） Josephson junctions （RCLSJJs） and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.展开更多
We investigate the dynamics of two tunnel-coupled Bose-Einstein condensates （BECs） in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal clo...We investigate the dynamics of two tunnel-coupled Bose-Einstein condensates （BECs） in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.展开更多
By introducing a discrete memristor and periodic sinusoidal functions,a two-dimensional map with coexisting chaos and hyperchaos is constructed.Various coexisting chaotic and hyperchaotic attractors under different Ly...By introducing a discrete memristor and periodic sinusoidal functions,a two-dimensional map with coexisting chaos and hyperchaos is constructed.Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map,along with which other regimes of coexistence such as coexisting chaos,quasiperiodic oscillation,and discrete periodic points are also captured.The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors.Based on the nonlinear auto-regressive model with exogenous inputs(NARX)for neural network,the dynamics of the memristive map is well predicted,which provides a potential passage in artificial intelligencebased applications.展开更多
Chaotic synchronization can be achieved by large enough external noise strength.It is shown that a pair of generic systems in the same potential evolving to equilibrium thr-ough standard Langevin dynamics with the sam...Chaotic synchronization can be achieved by large enough external noise strength.It is shown that a pair of generic systems in the same potential evolving to equilibrium thr-ough standard Langevin dynamics with the same noise collapse into the same orbits at longtime.We now extend the above idea to two identical hyperchaotic systems of generalizedvan der Pol oscillator.We then have Langevin equations as follows.展开更多
Lai and Grebogi demonstrated that by combining the Pecora-Carrool(drive-response)scheme(PISS)with the variable feedback synchronization(VFS),it is possible to synchronize two nearlyidentical hyperchaotic systems.This ...Lai and Grebogi demonstrated that by combining the Pecora-Carrool(drive-response)scheme(PISS)with the variable feedback synchronization(VFS),it is possible to synchronize two nearlyidentical hyperchaotic systems.This is called the drive-feedback synchronization(DFS).In thismethod,the feedback control is directly proportional to the difference of dynamical variable fromtwo hyperchaotie systems,and is applied to one of the systems.But in Lai and Grebogi’s work展开更多
The synchronization of chaotic nonlinear systems has attracted much attention in recent years.Practical applications are being realized in the area of secure communications.However,a few syn-chronization hyperchaos ha...The synchronization of chaotic nonlinear systems has attracted much attention in recent years.Practical applications are being realized in the area of secure communications.However,a few syn-chronization hyperchaos have been reported.We have extended the drive-response relationship scheme(DRRS)of chaotic synchronizationproposed by Pecora and Carroll to hyperchaos in the complex Lorenz-Haken system.But some-展开更多
基金supported by the National Natural Science Foundation of China (60971090)the Natural Science Foundation of Jiangsu Province (BK 2009105)
文摘To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz＇s, Chen＇s and Lu¨＇s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.24A0248)the National Key Research and Development Program“National Quality Infrastructure System”Special Project(Grant No.2024YFF0617900)the Hefei Minglong Electronic Technology Co.,Ltd.(Grant Nos.2024ZKHX293,2024ZKHX294,and 2024ZKHX295).
文摘Due to their biological interpretability,memristors are widely used to simulate synapses between artificial neural networks.As a type of neural network whose dynamic behavior can be explained,the coupling of resonant tunneling diode-based cellular neural networks(RTD-CNNs)with memristors has rarely been reported in the literature.Therefore,this paper designs a coupled RTD-CNN model with memristors(RTD-MCNN),investigating and analyzing the dynamic behavior of the RTD-MCNN.Based on this model,a simple encryption scheme for the protection of digital images in police forensic applications is proposed.The results show that the RTD-MCNN can have two positive Lyapunov exponents,and its output is influenced by the initial values,exhibiting multistability.Furthermore,a set of amplitudes in its output sequence is affected by the internal parameters of the memristor,leading to nonlinear variations.Undoubtedly,the rich dynamic behaviors described above make the RTD-MCNN highly suitable for the design of chaos-based encryption schemes in the field of privacy protection.Encryption tests and security analyses validate the effectiveness of this scheme.
基金Project supported by the Basic Scientific Research Projects of Department of Education of Liaoning Province,China(Grant No.LJ212410152049)the Technological Innovation Projects in the field of artificial intelligence of Liaoning Province,China(Grant No.2023JH26/10300011)。
文摘Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.
文摘This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.
基金Project supported by the National Nature Science Foundation of China （Grant No 60574036）, the Specialized Research Fund for the Doctoral Program of China （Grant No 20050055013） and the Program for New Excellent Talents in University of China （NCET）.
文摘This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.
基金The project supported by the National Natural Science Foundation of China
文摘Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as the origin of complexity of dynamical systems.
基金Projects(61073187,61161006) supported by the National Nature Science Foundation of ChinaProject supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,China
文摘To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62003177,61973172,61973175,and 62073177)the key Technologies Research and Tianjin Natural Science Foundation (Grant No.19JCZDJC32800)+1 种基金China Postdoctoral Science Foundation (Grant Nos.2020M670633 and 2020M670045)Academy of Finland (Grant No.315660)。
文摘Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.
文摘This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted （RCL-shunted） Josephson junctions （RCLSJJs） and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.
文摘We investigate the dynamics of two tunnel-coupled Bose-Einstein condensates （BECs） in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.
基金Project supported by the National Natural Science Foundation of China(Grant No.61871230)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20181410)the Postgraduate Research and Practice Innovation Project of Jiangsu Province,China(Grant No.SJCX210350).
文摘By introducing a discrete memristor and periodic sinusoidal functions,a two-dimensional map with coexisting chaos and hyperchaos is constructed.Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map,along with which other regimes of coexistence such as coexisting chaos,quasiperiodic oscillation,and discrete periodic points are also captured.The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors.Based on the nonlinear auto-regressive model with exogenous inputs(NARX)for neural network,the dynamics of the memristive map is well predicted,which provides a potential passage in artificial intelligencebased applications.
基金The project supported by China National Foundation of Nuclear Sciencethe National Project of Science and Technology for Returned Students
文摘Chaotic synchronization can be achieved by large enough external noise strength.It is shown that a pair of generic systems in the same potential evolving to equilibrium thr-ough standard Langevin dynamics with the same noise collapse into the same orbits at longtime.We now extend the above idea to two identical hyperchaotic systems of generalizedvan der Pol oscillator.We then have Langevin equations as follows.
基金The project supported by the Nuclear Industry Science Foundation of China and the National Project of Science and Technology for Returned Students.
文摘Lai and Grebogi demonstrated that by combining the Pecora-Carrool(drive-response)scheme(PISS)with the variable feedback synchronization(VFS),it is possible to synchronize two nearlyidentical hyperchaotic systems.This is called the drive-feedback synchronization(DFS).In thismethod,the feedback control is directly proportional to the difference of dynamical variable fromtwo hyperchaotie systems,and is applied to one of the systems.But in Lai and Grebogi’s work
基金The project supported by the China National Foundation of Nuclear Science and the National Project of Science and Technology for Returned Students
文摘The synchronization of chaotic nonlinear systems has attracted much attention in recent years.Practical applications are being realized in the area of secure communications.However,a few syn-chronization hyperchaos have been reported.We have extended the drive-response relationship scheme(DRRS)of chaotic synchronizationproposed by Pecora and Carroll to hyperchaos in the complex Lorenz-Haken system.But some-
