Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system

Gu, Shuangquan; He, Shaobo; Wang, Huihai; Du, Baoxiang

doi:10.1016/j.chaos.2020.110613

Cited by 46 publications

(15 citation statements)

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“…In addition, the system also has a variety of complex dynamic phenomena, including a multi-wing chaotic attractor [31][32][33], symmetric chaotic attractor [34][35][36], chaotic degradation, coexisting attractor and so on. Offset boosting [37][38][39] is also a feature of the system, which means that the system can be controlled flexibly through the introduction of feedback states. Finally, the feasibility of the system is verified by the DSP platform.…”

Section: Mathematical Modelmentioning

confidence: 99%

Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors

2022

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In this paper, a new six dimensional memristor chaotic system is designed by combining the chaotic system with a memristor. By analyzing the phase diagram of the chaotic attractors, eleven different attractors are found, including a multi-wing attractor and symmetric attractors. By analyzing the equilibrium point of the system, it is proven that the system has the property of a hidden chaotic attractor. The dynamic behavior of the system when the three parameters change is analyzed by means of LEs and a Bifurcation diagram. Other phenomenon, such as chaos degradation, coexistence of multiple attractors and bias boosting, are also found. Finally, the simulation on the DSP platform also verifies the accuracy of the chaotic system simulation. The theoretical analysis and simulation results show that the system has rich dynamical characteristics; therefore, it is suitable for secure communication and image encryption and other fields.

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Section: Mathematical Modelmentioning

confidence: 99%

Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors

2022

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“…In order to change this situation, Li [27] proposed a chaotic amplitude control method; by introducing a constant term into the system, ofset boosting can be achieved, which solves the problem of polarity conversion of chaotic signals; meanwhile, it does not change the dynamics of the system. Since then, many scholars have applied this method to the proposed chaotic systems, such as the ofset boosting control of the integer order chaotic attractor [28,29] and the fractional-order chaotic attractor [30,31]. Here, the original system is converted into a self-replicating system, resulting in an infnite number of attractors with extreme multistability.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamic Analysis, Circuit Design and Simplified Predefined Time Synchronization for a Jerk Absolute Memristor Chaotic System

et al. 2023

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In this parper, a 4D absolute memristor Jerk chaotic system is proposed. Firstly, complex dynamics are studied by phase diagram, Poincaré section, power spectrum, bifurcation diagram, 0-1 test, and Lyapunov exponent spectrum. Then, the period doubling bifurcation, degradation, and offset boosting are revealed. For the feasibility of practical application, the analog circuit and FPGA digital circuit are designed. Finally, a simplified predefined time synchronization scheme is proposed; comparing with the full control input synchronization scheme, the simplified predefined time synchronization scheme can not only reduce the controller inputs but also predefine the synchronization time.

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“…The analog implementation of Hindmarsh-Rose neuron model was discussed in [16]. Various dynamics of a fractional-order chaotic oscillator were investigated in [17]. The oscillator has three types of offset-boosting.…”

Section: Introductionmentioning

confidence: 99%

A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis

El‐Latif

Janarthanan

Abd-El-Atty³

et al. 2022

Mathematics

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Data security represents an essential task in the present day, in which chaotic models have an excellent role in designing modern cryptosystems. Here, a novel oscillator with chaotic dynamics is presented and its dynamical properties are investigated. Various properties of the oscillator, like equilibria, bifurcations, and Lyapunov exponents (LEs), are discussed. The designed system has a center point equilibrium and an interesting chaotic attractor. The existence of chaotic dynamics is proved by calculating Lyapunov exponents. The region of attraction for the chaotic attractor is investigated by plotting the basin of attraction. The oscillator has a chaotic attractor in which its basin is entangled with the center point. The complexity of the chaotic dynamic and its entangled basin of attraction make it a proper choice for image encryption. Using the effective properties of the chaotic oscillator, a method to construct pseudo-random numbers (PRNGs) is proposed, then utilizing the generated PRNG sequence for designing secure substitution boxes (S-boxes). Finally, a new image cryptosystem is presented using the proposed PRNG mechanism and the suggested S-box approach. The effectiveness of the suggested mechanisms is evaluated using several assessments, in which the outcomes show the characteristics of the presented mechanisms for reliable cryptographic applications.

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Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system

Cited by 46 publications

References 60 publications

Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors

Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors

Complex Dynamic Analysis, Circuit Design and Simplified Predefined Time Synchronization for a Jerk Absolute Memristor Chaotic System

A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis

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