Synchronization and antisynchronization of <i>N</i>‐coupled fractional‐order complex chaotic systems with ring connection

Jiang, Chen; Zhang, Fangfang; Li, Tongxing

doi:10.1002/mma.4765

Cited by 61 publications

(56 citation statements)

References 42 publications

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“…• The methods proposed in this paper can combine some statistical optimal strategies [47][48][49] to study the parameter estimation algorithms of linear and nonlinear systems [50][51][52][53][54][55][56] and can be extended to other fields. [57][58][59][60][61][62][63][64][65][66][67][68][69]…”

Section: Resultsmentioning

confidence: 99%

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

Ding

2019

Adaptive Control & Signal

170

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For a special class of nonlinear systems (ie, bilinear systems) with autoregressive moving average noise, this paper gives the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering-based maximum likelihood hierarchical gradient iterative algorithm and a filtering-based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient-based iterative algorithm and the multi-innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.

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Section: Resultsmentioning

confidence: 99%

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

Ding

2019

Adaptive Control & Signal

170

View full text Add to dashboard Cite

show abstract

“…The methods proposed in this paper can combine some statistical methods 47 to study the parameter identification and state filter design for different systems with colored noise [48][49][50][51][52][53][54][55] and can be applied to other fields. [56][57][58][59]…”

Section: Discussionmentioning

confidence: 99%

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

Ding

Sheng

2019

Adaptive Control & Signal

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Modeling an exponential autoregressive (ExpAR) time series is the basis of solving the corresponding prediction and control problems. This paper investigates the hierarchical parameter estimation methods for the ExpAR model.By the hierarchical identification principle, the original nonlinear optimization problem is transformed into the combination of a linear and nonlinear optimization problem, and then, we derive a hierarchical least squares and stochastic gradient (LS-SG) algorithm. Given the difficulty of determining the step-size in the hierarchical LS-SG algorithm, an approach is proposed to obtain the optimal step-size. To improve the parameter estimation accuracy, the multi-innovation identification theory is employed to develop a hierarchical least squares and multi-innovation stochastic gradient algorithm for the ExpAR model. Two simulation examples are provided to test the effectiveness of the proposed algorithms.

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“…Moghtadaei gave a complex Lorenz system in broad conception if there is at least one variable be complex variable. 22,23 The existing classical synchronization of complex chaotic systems mainly include in complete synchronization, 24,25 anti-synchronization, 26,27 projective synchronization, 28-30 dislocation synchronization, 31 phase synchronization, 32 delay synchronization, 33 and so on. 21 On the other hand, the chaos control and synchronization and its application in secure communication are studied.…”

Section: Introductionmentioning

confidence: 99%

Simplified method and synchronization for a class of complex chaotic systems

Huang

Zhang

Xiang

2019

Math Methods in App Sciences

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This paper is devoted to investigate a class of complex chaotic systems and a linear correlation between the real and imaginary component of complex variables in these systems is found. Based on this linear relationship, a simplified law is proposed. First, complex Lorenz system is given to show the linear correlation, then it is simplified. Second, a simplified law is proposed to determine whether the complex system can be simplified, and the complex Lü system and hyperchaotic complex Lü system are used to verify the simplified law.Finally, a new synchronization control is proposed to synchronize complex Lorenz system and real Lorenz system. The theoretical analysis and numerical simulation prove the feasibility and better performance of this method.

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Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Cited by 61 publications

References 42 publications

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

On some parameter estimation algorithms for the nonlinear exponential autoregressive model

Simplified method and synchronization for a class of complex chaotic systems

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