Synchronization of complex chaotic systems in series expansion form

2007 ◽  
Vol 34 (5) ◽  
pp. 1649-1658 ◽  
Author(s):  
Zheng-Ming Ge ◽  
Cheng-Hsiung Yang
Keyword(s):  
Series Expansion ◽  
Chaotic Systems ◽  
In Series ◽  
Expansion Form ◽  
Complex Chaotic Systems

scholarly journals Bayesian optimization for tuning chaotic systems

2014 ◽  
Vol 1 (2) ◽  
pp. 1283-1312
Author(s):  
M. Abbas ◽  
A. Ilin ◽  
A. Solonen ◽  
J. Hakkarainen ◽  
E. Oja ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Climate Models ◽  
Atmospheric Model ◽  
Bayesian Optimization ◽  
Tuning Parameters ◽  
Performance Metric ◽  
Weather And Climate ◽  
Computationally Expensive ◽  
Low Dimensional ◽  
Complex Chaotic Systems

Abstract. In this work, we consider the Bayesian optimization (BO) approach for tuning parameters of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a computationally expensive task. We show that BO, as a tool for finding the extrema of computationally expensive objective functions, is suitable for such tuning tasks. In the experiments, we consider tuning parameters of two systems: a simplified atmospheric model and a low-dimensional chaotic system. We show that BO is able to tune parameters of both the systems with a low number of objective function evaluations and without the need of any gradient information.

scholarly journals Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 481 ◽  
Author(s):  
Zhonghui Li ◽  
Tongshui Xia ◽  
Cuimei Jiang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Order Complex ◽  
Order Error ◽  
New Type ◽  
Modified Projective Synchronization ◽  
The Stability ◽  
Complex Chaotic Systems

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

scholarly journals Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Minglei Shu ◽  
Fangfang Zhang ◽  
Sen Leng ◽  
...  
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Digital Signal ◽  
Fractional Difference ◽  
Voice Signal ◽  
Difference Function ◽  
Image Cryptosystem ◽  
Definition Of ◽  
Complex Chaotic Systems ◽  
Function Synchronization

Fractional complex chaotic systems have attracted great interest recently. However, most of scholars adopted integer real chaotic system and fractional real and integer complex chaotic systems to improve the security of communication. In this paper, the advantages of fractional complex chaotic synchronization (FCCS) in secure communication are firstly demonstrated. To begin with, we propose the definition of fractional difference function synchronization (FDFS) according to difference function synchronization (DFS) of integer complex chaotic systems. FDFS makes communication secure based on FCCS possible. Then we design corresponding controller and present a general communication scheme based on FDFS. Finally, we respectively accomplish simulations which transmit analog signal, digital signal, voice signal, and image signal. Especially for image signal, we give a novel image cryptosystem based on FDFS. The results demonstrate the superiority and good performances of FDFS in secure communication.

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

2018 ◽  
Vol 28 (04) ◽  
pp. 1850050 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Xin Zhang ◽  
Wei Yao
Keyword(s):  
Fourth Order ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Random Bit Generator ◽  
In Series ◽  
Dynamical Features

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter [Formula: see text]. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

Module-phase synchronization of fractional-order complex chaotic systems based on RBF neural network and sliding mode control

2020 ◽  
Vol 34 (07) ◽  
pp. 2050050 ◽  
Author(s):  
Fuzhong Nian ◽  
Xinmeng Liu ◽  
Yaqiong Zhang ◽  
Xuelong Yu
Keyword(s):  
Neural Network ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Phase Synchronization ◽  
Sliding Mode ◽  
Rbf Neural Network ◽  
Order Complex ◽  
Mode Control ◽  
Complex Chaotic Systems

Combined with RBF neural network and sliding mode control, the synchronization between drive system and response system was achieved in module space and phase space, respectively (module-phase synchronization). The RBF neural network is used to estimate the unknown nonlinear function in the system. The module-phase synchronization of two fractional-order complex chaotic systems is implemented by the Lyapunov stability theory of fractional-order systems. Numerical simulations are provided to show the effectiveness of the analytical results.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

Sign in / Sign up

Export Citation Format

Share Document