This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
When a ceramic ionic-crystal nanocluster is group-substituted with polymer chain segments to form an ionomeric aggregate,is the ordered structure maintained within the sterically hindered nanocluster?We observed,for N...When a ceramic ionic-crystal nanocluster is group-substituted with polymer chain segments to form an ionomeric aggregate,is the ordered structure maintained within the sterically hindered nanocluster?We observed,for Na-salt sulfonated polystyrene ionomer,the electron-diffraction lattice fringes of the nanoclusters,which proved their internal crystalline ordering driven by electrostatic attractions overcoming steric hindrance.Kinetically,the nanoclusters'enhanced melting endotherm upon aging indicate their quasi-,slow-ordering character.Extended tight binding molecular dynamics simulations provide an insight into the mechanism underlying the ionic-group aggregation during nanoclustering.We hence proposed an uncommon state of order,polymer-bound ceramic quasicrystal,supplementary to the order phenomena in crystalline ceramics.展开更多
Molecular dynamics simulations were carried out to study the effect of chemical short-range order(CSRO)on the primary radiation damage in TiVTaNb high-entropy alloys(HEAs).We have performed displacement cascade simula...Molecular dynamics simulations were carried out to study the effect of chemical short-range order(CSRO)on the primary radiation damage in TiVTaNb high-entropy alloys(HEAs).We have performed displacement cascade simulations to explore the CSRO effect on the generation and evolution behaviors of irradiation defects.The results demonstrate that CSRO can suppress the formation of Frenkel pairs in TiVTaNb HEAs,with the suppression effect becoming more pronounced as the degree of CSRO increases.CSRO can change the types of interstitial defects generated during cascade collisions.Specifically,as the degree of CSRO increases,the proportion of Ti-related interstitials shows a marked enhancement,primarily evidenced by a significant rise in Ti–Ti dumbbells accompanied by a corresponding decrease in Ti–V dumbbells.CSRO exhibits negligible influence on defect clustering and the nucleation and evolution of dislocation loops.Regardless of CSRO conditions,TiVTaNb HEAs preserve exceptional radiation tolerance throughout the cascade damage process,suggesting that the intrinsic properties of this multi-principal element system dominate its radiation response.These findings provide fundamental insights into the CSRO effect on defect formation and evolution behaviors in HEAs,which may provide new design strategies for high-entropy alloys.展开更多
While 2D/3D heterostructures are widely employed to improve the stability of perovskite optoelectronic devices,their effectiveness is fundamentally governed by the crystallinity of the interfacial structure -a factor ...While 2D/3D heterostructures are widely employed to improve the stability of perovskite optoelectronic devices,their effectiveness is fundamentally governed by the crystallinity of the interfacial structure -a factor often overlooked.Disordered interfaces exhibit thermodynamic metastability,where ion diffusion induces sequential phase transitions from low-n to high-n phases.Here,we construct atomically ordered 2D/3D interfaces using phase-pure 2D perovskite capping layers,which reduce the interfacial phase transition rate by 95%and effectively suppress ion migration.As a result,devices exhibit outstanding operational stability,retaining over 99%of their initial power conversion efficiency after 1500 h of continuous operation,along with excellent thermal durability at 85℃.These findings identify interfacial order as a critical parameter for regulating ion dynamics and phase behavior,providing a robust design principle for achieving high-efficiency,long-lifetime perovskite technologies.展开更多
To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and...To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and scheme deviation degree as the optimization objectives.An adaptive dynamic scheduling strategy based on the degree of order disturbance is proposed.An improved multi-objective Grey Wolf(IMOGWO)optimization algorithm is designed by combining the“job-machine”two-layer encoding strategy,the timing-driven two-stage decoding strategy,the opposition-based learning initialization population strategy,the POX crossover strategy,the dualoperation dynamic mutation strategy,and the variable neighborhood search strategy for problem solving.A variety of test cases with different scales were designed,and ablation experiments were conducted to verify the effectiveness of the improved strategies.The results show that each improved strategy can effectively enhance the performance of the IMOGWO.Additionally,performance analysis was conducted by comparing the proposed algorithm with three mature and classical algorithms.The results demonstrate that the proposed algorithm exhibits superior performance in solving the hybrid flow-shop scheduling problem(HFSP).Case validations were conducted for different types of order disturbance scenarios.The results demonstrate that the proposed adaptive dynamic scheduling strategy and the IMOGWO algorithm can effectively address order disturbance events.They enable rapid response to order disturbance while ensuring the stability of the production system.展开更多
We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded...We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.展开更多
Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scalin...Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the desig...An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.展开更多
This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and extern...This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.展开更多
According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are construc...According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.展开更多
Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interac...Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.展开更多
This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that ...This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.展开更多
This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then in...This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.展开更多
A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed ...A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed through the approximation method of fractional order operator. In addition, it clearly describes the relationships between the impedance variation of the memristor and the varying mobility of the doped region of the memristor in different circuit parameters. Finally, a periodic memristor-based system driven by another chaotic memristor-based fractional order system is synchronized to chaotic state via the linear error feedback technique.展开更多
A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. ...A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.展开更多
In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy u...In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy used the robust Fractional-Order(FO)Proportional-Integral(PI)control technique.The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits.It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness.The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization(MRFO)algorithm.During the optimization process,the FOPI controller’s parameters are assigned to be the decision variables whereas the objective function is the error racking that to be minimized.To prove the superiority of the MRFO algorithm,an empirical comparison study with the homologous particle swarm optimization and genetic algorithm is achieved.The obtained results proved the superiority of the introduced strategy in tracking and control performances against various conditions such as voltage dips and wind speed variation.展开更多
This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtai...This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtain a stable reduced order system, the stable model order reduction procedure is discussed. By the revised operation on the tridiagonal matrix produced by the unsymmetric Lanczos algorithm, we propose a reduced order modeling method for a fractional-order system to achieve a satisfactory fitting effect with the original system by the matched moments in the frequency domain. Besides, the bound function of the order reduction error is offered. Two numerical examples are presented to illustrate the effectiveness of the proposed method.展开更多
This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a syn...This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.展开更多
In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-or...In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.展开更多
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
基金Funded by the Hubei Province Key Research Foundation for Water Resources,China(No.HBSLKY2023035)as well as by the Technology Foundation for Selected Overseas Scholars,Ministry of Human Resources and Social Security,China(No.[2013]277)+2 种基金the Natural Science Foundation of the Hubei Province of China(No.2014CFA094)the Overseas High-level Talents Scientific-research Starting Fund of Hubei University of Technology,China(HBUTscience-[2005]2)the National Natural Science Foundation of China(No.51703053)。
文摘When a ceramic ionic-crystal nanocluster is group-substituted with polymer chain segments to form an ionomeric aggregate,is the ordered structure maintained within the sterically hindered nanocluster?We observed,for Na-salt sulfonated polystyrene ionomer,the electron-diffraction lattice fringes of the nanoclusters,which proved their internal crystalline ordering driven by electrostatic attractions overcoming steric hindrance.Kinetically,the nanoclusters'enhanced melting endotherm upon aging indicate their quasi-,slow-ordering character.Extended tight binding molecular dynamics simulations provide an insight into the mechanism underlying the ionic-group aggregation during nanoclustering.We hence proposed an uncommon state of order,polymer-bound ceramic quasicrystal,supplementary to the order phenomena in crystalline ceramics.
基金Project supported by the Youth Program of the National Natural Science Foundation of China(Grant No.12405324)the CNNC Science Fund for Talented Young Scholars(Grant No.24940)the CNNC Basic Science Fund(Grant No.24851)。
文摘Molecular dynamics simulations were carried out to study the effect of chemical short-range order(CSRO)on the primary radiation damage in TiVTaNb high-entropy alloys(HEAs).We have performed displacement cascade simulations to explore the CSRO effect on the generation and evolution behaviors of irradiation defects.The results demonstrate that CSRO can suppress the formation of Frenkel pairs in TiVTaNb HEAs,with the suppression effect becoming more pronounced as the degree of CSRO increases.CSRO can change the types of interstitial defects generated during cascade collisions.Specifically,as the degree of CSRO increases,the proportion of Ti-related interstitials shows a marked enhancement,primarily evidenced by a significant rise in Ti–Ti dumbbells accompanied by a corresponding decrease in Ti–V dumbbells.CSRO exhibits negligible influence on defect clustering and the nucleation and evolution of dislocation loops.Regardless of CSRO conditions,TiVTaNb HEAs preserve exceptional radiation tolerance throughout the cascade damage process,suggesting that the intrinsic properties of this multi-principal element system dominate its radiation response.These findings provide fundamental insights into the CSRO effect on defect formation and evolution behaviors in HEAs,which may provide new design strategies for high-entropy alloys.
基金funding supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB1140000)National Natural Science Foundation of China(22379156,U23A20141)+1 种基金Qingdao New Energy Shandong Laboratory(QIBEBT/SEI/QNESL S202305)Key R&D Program of Shandong Province,China(2024SFGC0102)。
文摘While 2D/3D heterostructures are widely employed to improve the stability of perovskite optoelectronic devices,their effectiveness is fundamentally governed by the crystallinity of the interfacial structure -a factor often overlooked.Disordered interfaces exhibit thermodynamic metastability,where ion diffusion induces sequential phase transitions from low-n to high-n phases.Here,we construct atomically ordered 2D/3D interfaces using phase-pure 2D perovskite capping layers,which reduce the interfacial phase transition rate by 95%and effectively suppress ion migration.As a result,devices exhibit outstanding operational stability,retaining over 99%of their initial power conversion efficiency after 1500 h of continuous operation,along with excellent thermal durability at 85℃.These findings identify interfacial order as a critical parameter for regulating ion dynamics and phase behavior,providing a robust design principle for achieving high-efficiency,long-lifetime perovskite technologies.
基金funded by National Key Research and Development Program Projects of China under Grant No.2020YFB1713500.
文摘To address the issue that hybrid flow shop production struggles to handle order disturbance events,a dynamic scheduling model was constructed.The model takes minimizing the maximum makespan,delivery time deviation,and scheme deviation degree as the optimization objectives.An adaptive dynamic scheduling strategy based on the degree of order disturbance is proposed.An improved multi-objective Grey Wolf(IMOGWO)optimization algorithm is designed by combining the“job-machine”two-layer encoding strategy,the timing-driven two-stage decoding strategy,the opposition-based learning initialization population strategy,the POX crossover strategy,the dualoperation dynamic mutation strategy,and the variable neighborhood search strategy for problem solving.A variety of test cases with different scales were designed,and ablation experiments were conducted to verify the effectiveness of the improved strategies.The results show that each improved strategy can effectively enhance the performance of the IMOGWO.Additionally,performance analysis was conducted by comparing the proposed algorithm with three mature and classical algorithms.The results demonstrate that the proposed algorithm exhibits superior performance in solving the hybrid flow-shop scheduling problem(HFSP).Case validations were conducted for different types of order disturbance scenarios.The results demonstrate that the proposed adaptive dynamic scheduling strategy and the IMOGWO algorithm can effectively address order disturbance events.They enable rapid response to order disturbance while ensuring the stability of the production system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61004078 and 60971022)the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2009GQ009 and ZR2009GM005)+1 种基金the China Postdoctoral Science Foundation (Grant No. 20100481293)the Special Funds for Postdoctoral Innovative Projects of Shandong Province, China (Grant No. 201003037)
文摘We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.
基金Project supported by the National Natural Science Foundation of China(Grant No.11371049)the Science Foundation of Beijing Jiaotong University(Grant Nos.2011JBM130 and 2011YJS076)
文摘Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
基金Project supported by the Research Foundation of Education Bureau of Hebei Province,China(Grant No.QN2014096)
文摘An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.
文摘This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.
基金Sponsored by the National Natural Sciences Foundation of China(Grant No.61201227)
文摘According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.
文摘Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.
文摘This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.
文摘This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.
文摘A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed through the approximation method of fractional order operator. In addition, it clearly describes the relationships between the impedance variation of the memristor and the varying mobility of the doped region of the memristor in different circuit parameters. Finally, a periodic memristor-based system driven by another chaotic memristor-based fractional order system is synchronized to chaotic state via the linear error feedback technique.
基金Project supported by the Center for Nonlinear Systems,Chennai Institute of Technology,India (Grant No. CIT/CNS/2020/RD/061)。
文摘A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.
文摘In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy used the robust Fractional-Order(FO)Proportional-Integral(PI)control technique.The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits.It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness.The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization(MRFO)algorithm.During the optimization process,the FOPI controller’s parameters are assigned to be the decision variables whereas the objective function is the error racking that to be minimized.To prove the superiority of the MRFO algorithm,an empirical comparison study with the homologous particle swarm optimization and genetic algorithm is achieved.The obtained results proved the superiority of the introduced strategy in tracking and control performances against various conditions such as voltage dips and wind speed variation.
基金supported by the National Natural Science Foundation of China(61304094,61673198,61773187)the Natural Science Foundation of Liaoning Province,China(20180520009)
文摘This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtain a stable reduced order system, the stable model order reduction procedure is discussed. By the revised operation on the tridiagonal matrix produced by the unsymmetric Lanczos algorithm, we propose a reduced order modeling method for a fractional-order system to achieve a satisfactory fitting effect with the original system by the matched moments in the frequency domain. Besides, the bound function of the order reduction error is offered. Two numerical examples are presented to illustrate the effectiveness of the proposed method.
文摘This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.
文摘In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.
