A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability ...A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.展开更多
This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which...This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronizution law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.展开更多
This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system...This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.展开更多
In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control...In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.展开更多
In the recent years, researchers developed image encryption methods based on chaotic systems. This paper proposed new image encryption technique based on new chaotic system by adding two chaotic systems: the Lorenz ch...In the recent years, researchers developed image encryption methods based on chaotic systems. This paper proposed new image encryption technique based on new chaotic system by adding two chaotic systems: the Lorenz chaotic system and the R?ssler chaotic system. The main advantage of this technique is stronger security, as is shown in the encryption tests.展开更多
The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind ...The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.展开更多
Nowadays,high-resolution images pose several challenges in the context of image encryption.The encryption of huge images’file sizes requires high computational resources.Traditional encryption techniques like,Data En...Nowadays,high-resolution images pose several challenges in the context of image encryption.The encryption of huge images’file sizes requires high computational resources.Traditional encryption techniques like,Data Encryption Standard(DES),and Advanced Encryption Standard(AES)are not only inefficient,but also less secure.Due to characteristics of chaos theory,such as periodicity,sensitivity to initial conditions and control parameters,and unpredictability.Hence,the characteristics of deoxyribonucleic acid(DNA),such as vast parallelism and large storage capacity,make it a promising field.This paper presents an efficient color image encryption method utilizing DNA encoding with two types of hyper-chaotic maps.The proposed encryption method comprises three steps.The first step initializes the conditions for generating Lorenz and Rossler hyper-chaotic maps using a plain image Secure Hash Algorithm(SHA-256/384).The second step performs a confusion procedure by scrambling the three components of the image(red,green,and blue)using Lorenz hyper-chaotic sequences.Finally,the third step combines three approaches to encrypt the scrambled components for diffusion:DNA encoding/decoding,addition operation between components,and XORing with Rossler hyper-chaotic sequences.The simulation results indicate that the suggested encryption algorithm satisfies the requirements of security.The entropy value of confusion and diffusion is 7.997,the key space is 2200,and the correlation coefficient is nearly zero.The efficacy of the proposed method has been verified through numerous evaluations,and the results show its resistance and effectiveness against several attacks,like statistical and brute-force attacks.Finally,the devised algorithm vanquishes other relevant color image encryption algorithms.展开更多
Community-acquired pneumonia(CAP)is considered a sort of pneumonia developed outside hospitals and clinics.To diagnose community-acquired pneumonia(CAP)more efficiently,we proposed a novel neural network model.We intr...Community-acquired pneumonia(CAP)is considered a sort of pneumonia developed outside hospitals and clinics.To diagnose community-acquired pneumonia(CAP)more efficiently,we proposed a novel neural network model.We introduce the 2-dimensional wavelet entropy(2d-WE)layer and an adaptive chaotic particle swarm optimization(ACP)algorithm to train the feed-forward neural network.The ACP uses adaptive inertia weight factor(AIWF)and Rossler attractor(RA)to improve the performance of standard particle swarm optimization.The final combined model is named WE-layer ACP-based network(WACPN),which attains a sensitivity of 91.87±1.37%,a specificity of 90.70±1.19%,a precision of 91.01±1.12%,an accuracy of 91.29±1.09%,F1 score of 91.43±1.09%,an MCC of 82.59±2.19%,and an FMI of 91.44±1.09%.The AUC of this WACPN model is 0.9577.We find that the maximum deposition level chosen as four can obtain the best result.Experiments demonstrate the effectiveness of both AIWF and RA.Finally,this proposed WACPN is efficient in diagnosing CAP and superior to six state-of-the-art models.Our model will be distributed to the cloud computing environment.展开更多
In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the control...In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.展开更多
This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler l...This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.展开更多
In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relatio...In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relationship between the shape （including the range and the number of stripes） and some parameters is discussed. The result shows that noise can also generate the striped shape effectively and simply, which is similar to the newly-discovered striped pattern generated by controlled Rossler systems.展开更多
Phase synchronization between nonlinearly coupled systems with 1：1 and 1：2 resonances is investigated. By introducing a concept of phase for a chaotic motion, it is demonstrated that for different internal resonance...Phase synchronization between nonlinearly coupled systems with 1：1 and 1：2 resonances is investigated. By introducing a concept of phase for a chaotic motion, it is demonstrated that for different internal resonances, with relatively small parameter epsilon, the difference between the mean frequencies of the two sub-oscillators approaches zero. This implies that phase synchronization can be achieved for weak interaction between the two oscillators. With the increase in coupling strength, fluctuations of the frequency difference can be observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared to the case with frequency ratio 1：2, even with the weak coupling strength. Unlike the enhanced effect on synchronization for linear coupling, the increase in nonlinear coupling strength results in the transition from phase synchronization to a non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Lyapunov exponents, which can also be explained with the diffuse clouds.展开更多
The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies,...The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,展开更多
In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expres...In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expressed in the system. The analysis and proof are given by means of the Lyapunov stability theorem. Based on theoretical analysis, some sufficient conditions of complete synchronization are proved. In order to validate the proposed scheme, numerical simulations are performed and the numerical results show that our scheme is very effective.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
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
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asympto...The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.展开更多
Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to ...Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 20373021） and Natural Science Foundation of Liaoning Province （Grant No 20052151）.
文摘A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.
基金Project supported by the Major Program of the National Natural Science Foundation of China （Grant No 60271019）, the Doctorate Foundation of the Ministry of Education of China （Grant No 20020611007）.
文摘This paper reports that an impulsive control theory for synchronization of nonlinear Rossler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronizution law. The proposed impulsive control scheme is illustrated by nonlinear Rossler chaotic systems and the simulation results demonstrate the effectiveness of the method.
基金Project supported by the Key Youth Project of Southwest University for Nationalities of China and the Natural Science Foundation of the State Nationalities Affairs Commission of China （Grant Nos 05XN07 and 07XN05）.
文摘This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.
基金Project supported by the Natural Science Foundation of Yangzhou University of China （Grant No KK0513109）.
文摘In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.
文摘In the recent years, researchers developed image encryption methods based on chaotic systems. This paper proposed new image encryption technique based on new chaotic system by adding two chaotic systems: the Lorenz chaotic system and the R?ssler chaotic system. The main advantage of this technique is stronger security, as is shown in the encryption tests.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262006 and 11062002)the Science and Technology Project of Jiangxi Province,China(Grant Nos.GJJ12330 and 2010GQW0021)
文摘The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.
基金This research is funded by Universiti SainsMalaysia(USM)via an external Grant Number(304/PNAV/650958/U154).
文摘Nowadays,high-resolution images pose several challenges in the context of image encryption.The encryption of huge images’file sizes requires high computational resources.Traditional encryption techniques like,Data Encryption Standard(DES),and Advanced Encryption Standard(AES)are not only inefficient,but also less secure.Due to characteristics of chaos theory,such as periodicity,sensitivity to initial conditions and control parameters,and unpredictability.Hence,the characteristics of deoxyribonucleic acid(DNA),such as vast parallelism and large storage capacity,make it a promising field.This paper presents an efficient color image encryption method utilizing DNA encoding with two types of hyper-chaotic maps.The proposed encryption method comprises three steps.The first step initializes the conditions for generating Lorenz and Rossler hyper-chaotic maps using a plain image Secure Hash Algorithm(SHA-256/384).The second step performs a confusion procedure by scrambling the three components of the image(red,green,and blue)using Lorenz hyper-chaotic sequences.Finally,the third step combines three approaches to encrypt the scrambled components for diffusion:DNA encoding/decoding,addition operation between components,and XORing with Rossler hyper-chaotic sequences.The simulation results indicate that the suggested encryption algorithm satisfies the requirements of security.The entropy value of confusion and diffusion is 7.997,the key space is 2200,and the correlation coefficient is nearly zero.The efficacy of the proposed method has been verified through numerous evaluations,and the results show its resistance and effectiveness against several attacks,like statistical and brute-force attacks.Finally,the devised algorithm vanquishes other relevant color image encryption algorithms.
基金This paper is partially supported by Medical Research Council Confidence in Concept Award,UK(MC_PC_17171)Royal Society International Exchanges Cost Share Award,UK(RP202G0230)+5 种基金British Heart Foundation Accelerator Award,UK(AA/18/3/34220)Hope Foundation for Cancer Research,UK(RM60G0680)Global Challenges Research Fund(GCRF),UK(P202PF11)Sino-UK Industrial Fund,UK(RP202G0289)LIAS Pioneering Partnerships award,UK(P202ED10)Data Science Enhancement Fund,UK(P202RE237).
文摘Community-acquired pneumonia(CAP)is considered a sort of pneumonia developed outside hospitals and clinics.To diagnose community-acquired pneumonia(CAP)more efficiently,we proposed a novel neural network model.We introduce the 2-dimensional wavelet entropy(2d-WE)layer and an adaptive chaotic particle swarm optimization(ACP)algorithm to train the feed-forward neural network.The ACP uses adaptive inertia weight factor(AIWF)and Rossler attractor(RA)to improve the performance of standard particle swarm optimization.The final combined model is named WE-layer ACP-based network(WACPN),which attains a sensitivity of 91.87±1.37%,a specificity of 90.70±1.19%,a precision of 91.01±1.12%,an accuracy of 91.29±1.09%,F1 score of 91.43±1.09%,an MCC of 82.59±2.19%,and an FMI of 91.44±1.09%.The AUC of this WACPN model is 0.9577.We find that the maximum deposition level chosen as four can obtain the best result.Experiments demonstrate the effectiveness of both AIWF and RA.Finally,this proposed WACPN is efficient in diagnosing CAP and superior to six state-of-the-art models.Our model will be distributed to the cloud computing environment.
基金Project supported by the National Natural Science Foundation of China (Grant No 60574011)
文摘In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.
文摘This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.
文摘In this paper, the generation of striped trajectories in phase space by noise-injection is considered. With suitable amplitudes of noise, the steady-state system orbits appear in rectangular striped shape. The relationship between the shape （including the range and the number of stripes） and some parameters is discussed. The result shows that noise can also generate the striped shape effectively and simply, which is similar to the newly-discovered striped pattern generated by controlled Rossler systems.
基金Project supported by the National Natural Science Foundation of China (Nos.20476041,10602020)
文摘Phase synchronization between nonlinearly coupled systems with 1：1 and 1：2 resonances is investigated. By introducing a concept of phase for a chaotic motion, it is demonstrated that for different internal resonances, with relatively small parameter epsilon, the difference between the mean frequencies of the two sub-oscillators approaches zero. This implies that phase synchronization can be achieved for weak interaction between the two oscillators. With the increase in coupling strength, fluctuations of the frequency difference can be observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared to the case with frequency ratio 1：2, even with the weak coupling strength. Unlike the enhanced effect on synchronization for linear coupling, the increase in nonlinear coupling strength results in the transition from phase synchronization to a non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Lyapunov exponents, which can also be explained with the diffuse clouds.
基金Project supported by the National Basic Research Project"Nonlinear Science"of Chinathe National Natural Science Foundation of China
文摘The problem of how to control chaos has attracted a great deal of attention. A simplemethod is to suppress chaos by periodic perturbations. This method has already beenapplied to nonautonomous systems in most studies, but seldom is it used to treat the au-tonomous systems and cases without motion equations. Based on one-dimensional maps,
基金Project supported by the National Natural Science Foundation of China (Grant No.10847110)
文摘In this paper, we investigate complete synchronization of double-delayed RSssler systems with uncertain parameters as the master system is in chaotic synchronization. The uncertain parameters can be nonlinearly expressed in the system. The analysis and proof are given by means of the Lyapunov stability theorem. Based on theoretical analysis, some sufficient conditions of complete synchronization are proved. In order to validate the proposed scheme, numerical simulations are performed and the numerical results show that our scheme is very effective.
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-
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
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
基金Project supported by National Natural Science Foundation of China （Grant No 60274032）, and Science and Technology Rising-Star Program of Shanghai, China （Grant No 04QMH1405）.
文摘The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.
文摘Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.
