N-Systems Function Projective Combination Synchronization—A Review of Real and Complex Continuous Time Chaos Synchronization

In this paper, a methodology to design a system that robustly synchronizes a master chaotic system from a sampled driving signal is developed. The method is based on the fuzzy Takagi–Sugeno representation of chaotic systems, from which a continuous-time fuzzy observer is designed as the solution of an LMI minimization problem such that the error dynamics have H∞disturbance attenuation performance. Then, from the dual-system approach, the fuzzy observer is digitally redesigned such that the performance is maintained for the sampled master system. The effectiveness of the proposed synchronization methodology is finally illustrated via numerical simulations of the chaotic Chen's system.

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Study on Discreted Fifth-Order CNN Hyper-Chaos Synchronization Reduced Order Observer

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.135-136.960 ◽

2011 ◽

Vol 135-136 ◽

pp. 960-963

Author(s):

Jie Xu ◽

Juan Chang ◽

Lian Zhang ◽

Yong Sun

Keyword(s):

Neural Networks ◽

Continuous Time ◽

Secure Communication ◽

Chaos Synchronization ◽

State Observer ◽

Cellular Neural Networks ◽

Reduced Order ◽

Reduced Order Observer ◽

Fifth Order ◽

Order State

Secure communication with the hyper-chaos synchronization approach is the popular investigation. In this paper the fifth-order Cellular Neural Networks(CNN) hyper-chaos equation of continuous time was discreted. The innovation was that the synchronization of the hyper-chaos system was realized with the discreted reduced order state observer. Finally, the system stabilizing to zero after fugacious transition and achieving synchronization were validated by simulations, which showed the algorithm’s availability.

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HYBRID CHAOS SYNCHRONIZATION

International Journal of Bifurcation and Chaos ◽

10.1142/s021812740300714x ◽

2003 ◽

Vol 13 (05) ◽

pp. 1197-1216 ◽

Cited By ~ 18

Author(s):

JUAN-GONZALO BARAJAS-RAMÍREZ ◽

GUANRONG CHEN ◽

LEANG S. SHIEH

Keyword(s):

Continuous Time ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Duffing Oscillator ◽

The Novel ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Digital Redesign ◽

Different Chaotic Systems ◽

Novel Design

The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chaotic systems, Chua's circuit, Duffing oscillator, and Chen's system, are simulated thereby validating the novel design proposed in this paper.

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Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Journal of Applied Probability ◽

10.1017/s0021900200002965 ◽

2007 ◽

Vol 44 (02) ◽

pp. 285-294 ◽

Cited By ~ 2

Author(s):

Qihe Tang

Keyword(s):

Asymptotic Formula ◽

Continuous Time ◽

Heavy Tails ◽

Tail Behavior ◽

Renewal Model ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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