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1.
In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis. 相似文献
2.
In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results. 相似文献
3.
Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems
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We investigate the synchronization of a class of incommensurate fractional-order chaotic systems,and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory,the fractional order differential inequality,and the adaptive strategy.This synchronization approach is simple,universal,and theoretically rigorous.It enables the synchronization of0 fractional-order chaotic systems to be achieved in a systematic way.The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme. 相似文献
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In this paper, a function cascade synchronization method for fractional-order hyperchaotic systems is introduced to achieve the synchronization of two identical fractional-order hyperchaotic systems. It is shown that the method is not only theoretically rigorous, practically feasible, but also a more general one, which contains the complete synchronization, modified projective synchronization and anti-phase synchronization. In order to valid the effectiveness of the proposed method, we give two illustrative examples. Suitable controllers are designed and the function cascade synchronization for fractional-order hyperchaotic systems is achieved. Numerical simulations are performed and shown to fit with our analysis results. 相似文献
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Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system. 相似文献
8.
《Chinese Journal of Physics (Taipei)》2018,56(5):2553-2559
The scheme of synchronization between fractional-order chaotic systems with non-identical orders, unknown parameters and disturbances was investigated. A sliding surface was defined based on the theory of sliding mode control and a controller with adaptive laws was designed based on the stability of fractional-order nonlinear systems. The synchronization of two fractional-order hyperchaotic systems was simulated by using the fractional differential transform method to validate the effectiveness and the feasibility of the proposed scheme. All the theoretical analysis and simulation results showed the effectiveness of the proposed scheme. 相似文献
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Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)
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Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well. 相似文献
11.
Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems 总被引:1,自引:0,他引:1
In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method. 相似文献
12.
A new stability theory of nonlinear dynamic systems is
proposed, and a novel adaptive synchronisation method is presented
for fractional-order chaotic and hyperchaotic systems based on the
theory described in this paper. In comparison with previous methods,
not only is the present control scheme simple but also it employs
only one control strength, converges very fast, and it is also
suitable for a large class of fractional-order chaotic and
hyperchaotic systems. Moreover, this scheme is analytical and simple
to implement in practice. Numerical and circuit simulations are
used to validate and demonstrate the effectiveness of the method. 相似文献
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《中国物理 B》2015,(9)
In this paper the synchronization for two different fractional-order chaotic systems, capable of guaranteeing synchronization error with prescribed performance, is investigated by means of the fractional-order control method. By prescribed performance synchronization we mean that the synchronization error converges to zero asymptotically, with convergence rate being no less than a certain prescribed function. A fractional-order synchronization controller and an adaptive fractional-order synchronization controller, which can guarantee the prescribed performance of the synchronization error,are proposed for fractional-order chaotic systems with and without disturbances, respectively. Finally, our simulation studies verify and clarify the proposed method. 相似文献
15.
Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems
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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. 相似文献
16.
Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay
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This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay. The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated. Meanwhile, based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems, a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks. Finally, the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme. 相似文献
17.
Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller
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<正>In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integerorder chaotic system,in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method.Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus.Moreover,three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results.Finally,results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems. 相似文献
18.
《Chinese Journal of Physics (Taipei)》2017,55(2):342-349
This paper deals with the drive-response synchronization scheme for uncertain fractional-order chaotic systems. Some novel sufficient conditions for chaos synchronization of fractional-order chaotic systems with model uncertainties and external disturbances are derived by using the fractional-order extension of the Lyapunov stability theorem. The designed synchronization are new, simple and yet easily realized experimentally compared with those where complex control functions are used. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme. 相似文献
19.
In this paper the synchronization of fractional-order chaotic systems is studied and a new single state fractional-order chaotic controller for chaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can apply to an arbitrary three-dimensional fractional chaotic system whether the system is incommensurate or commensurate. This approach is universal, simple and theoretically rigorous. Numerical simulations of several fractional-order chaotic systems demonstrate the universality and the effectiveness of the proposed method. 相似文献
20.
In this paper,a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed.Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved.The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis. 相似文献