Chaos Theory and Applications

This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.

Michael Kopp

Inna Samuilik

A New 6D Two-wing Hyperhaotic System: Dynamical Analysis, Circuit Design, and Sinchronization

一个新的6维双翼超混沌系统：动力学分析、电路设计与同步

This paper proposes an entropy-sensitive based data coding algorithm for the secure communication of image information between transceiver systems. The proposed algorithm utilizes chaos theory as well as image information content of reference image in order to create sensitivity on decoding side for the high level of secrecy. This article aims to recover secret images at the receiver side by using secret code series related both secret and reference images, instead of direct transmission. The code series used in the algorithm depends on the parameters of the chaotic Logistic map and entropy of the reference image. The image information can be retrieved only through the same reference image, same system parameters and identical code series under the proper decoding technique in the receiver side. Moreover, the proposed algorithm offers high sensitivity to the reference image and the parameters of the chaotic system in such way that if a single bit change in any pixel of the reference image, the secret image cannot be recovered even with the same system parameters of the decoding algorithm. Experimental results on various images show that the proposed algorithm is reliable, fast and effective in securing confidential image information.

Hidayet Oğraş

A New Data Coding Algorithm for Secure Communication of Image

一种新的图像安全通信数据编码算法

In this manuscript, we establish hybrid function projective synchronization of a new hyperchaotic system using an adaptive control technique with unknown system parameters. In order to prevent either from deriving from participants in the single hyperchaotic financial system, identical master and slave systems are chosen. We design an adaptive controller to achieve global chaos synchronization between these master and slave systems. The synchronization results are based on adaptive control theory and Lyapunov stability theory. Additionally, we outline the basic dynamic characteristics of both hyperchaotic financial systems. Numerical simulations performed in Matlab validate our results excellently.

Vikash .

Ayub Khan

Khursheed Alam

Hybrid Function Projective Synchronization of Hyperchaotic Financial Systems via Adaptive Control

超混沌金融系统的混合函数投影同步及自适应控制

This research explores the application of kernel estimation method in analyzing the ratio of taxpayer audit to total taxpayers, and provides insight into the distribution of taxpayer audits and their impact on tax compliance. The ’find distribution’ uses to model the artificial data generated from kernel smooth functions. The study uses simulated data to evaluate two significant populations of both audit and total taxpayers especially when the maximum statistics are observed importantly: one block of about 80,000 taxpayer audit and the other of about 100,000, and similarly, one block of total taxpayers of about 4.5 million and the other of about 6 million. When the results for the maximum number of taxable persons and taxpayers are compared, the more taxable persons lead to the detection of the more taxpayer audit. The reason for choosing the maximum statistics is that it may give us a clearer picture both in the near future and in determining the required number of taxpayers. The dataset also includes other statistics, such as the weighted mean for taxpayer audit and the number of taxpayer, which are approximately 75,000 and 4 million respectively, providing a summary of the overall characteristics of the dataset. These findings suggest that different number of taxpayer populations exist and can behave in versatile forms and highlight the need for targeted audit strategies. The study highlights the importance of using sophisticated statistical methods to accurately model these complex, multimodal data distributions which can be modelled by using the kernel estimation method. By improving our understanding of these populations, policymakers and tax authorities can implement more effective policies to optimize tax audit processes and ensure fair tax compliance among different taxpayer groups.

Mehmet Niyazi Çankaya

Murat Aydın

Tax Audit in Turkiye: Simulation and Estimations Based on Kernel and Weight Functions

土耳其的税务审计：基于核函数和权重函数的模拟与估计

The chaotic systems are one of the most important areas that increasing the popularity and are actively used in several fields. One of the most essential structures in chaotic systems is chaotic oscillator which generates chaotic signals. IQ-Math and floating point number systems are one of the preferred number standards. Presented in this study, the Modified Chua chaotic oscillator has been designed to work on FPGA chips using fixed point and floating point number systems. Euler numeric algorithm has been used for the design of the Modified Chua chaotic oscillator. The first section of the study, Modified Chua chaotic system based on fixed point has been composed the model in the Matlab Simulink and transformed to VHDL with the help of Matlab HDL Coder Toolbox. The second section of the study, Modified Chua chaotic oscillator has been designed with VHDL based on floating point. Modified Chua chaotic oscillators which are composed with two different number standards have been tested using Xilinx ISE Design Tools in VHDL. Modified Chua chaotic oscillators which have two different numbers standards and designed, are synthesized for Virtex-6 on ML605 FPGA development board with Xilinx ISE Design Tools 14.2 program. Values that are achieved from the process of synthesizing and maximum operating frequency have been presented. As a result, the study has obtained that fixed point number standard maximum operating frequency is 50.242 MHz and floating point number standard maximum operating frequency is 273.631 MHz.

ISSN	2687-4539
h-index	11

Publication Information	Publisher: Akif AKGUL，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2019，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:
Journal Fees	$550Details
Average review cycle	18 weeks

Chaos Theory and Applications

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A New 6D Two-wing Hyperhaotic System: Dynamical Analysis, Circuit Design, and Sinchronization

A New Data Coding Algorithm for Secure Communication of Image

Hybrid Function Projective Synchronization of Hyperchaotic Financial Systems via Adaptive Control

Tax Audit in Turkiye: Simulation and Estimations Based on Kernel and Weight Functions

Performance Evaluation of FPGA-Based Design of Modified Chua Oscillator

A New Data Coding Algorithm for Secure Communication of Image

A New 6D Two-wing Hyperhaotic System: Dynamical Analysis, Circuit Design, and Sinchronization

Tax Audit in Turkiye: Simulation and Estimations Based on Kernel and Weight Functions

Performance Evaluation of FPGA-Based Design of Modified Chua Oscillator

Hybrid Function Projective Synchronization of Hyperchaotic Financial Systems via Adaptive Control