High-complex chaotic system based on new nonlinear function and OTA-based circuit realization

Karawanich, Khunanon; Prommee, Pipat

doi:10.1016/j.chaos.2022.112536

Cited by 14 publications

(5 citation statements)

References 42 publications

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“…which is a half-line consisting of the non-positive x-axis in R 4 We have used Wolf's approach [33] to determine the Lyapunov exponents of system (11) for the initial state (0.2, 0.2, 0.2, 0.2) and the parameter values a = 4 and b = 2. The four Lyapunov exponents of the novel 4-D system (11) were calculated as follows:…”

Section: A New Hyperjerk System With a Half Line Equilibriummentioning

confidence: 99%

“…This means that even small differences in the initial states of a chaotic system can lead to drastically different outcomes over time ( [2], [3]). In other words, tiny changes in the starting conditions can lead to divergent trajectories that seem unpredictable and random, even though the system is deterministic and follows specific rules [4]. In addition, chaotic systems can be found in various fields, including physics, meteorology, biology, economics, and engineering.…”

Section: Introductionmentioning

confidence: 99%

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A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

Sambas,

Miroslav,

Vaidyanathan

et al. 2024

IEEE Access

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A hyperjerk system pertains to a dynamical system regulated by an ordinary differential equation of nth order, where n ≥ 4. The main contribution of this work is the finding of a new autonomous hyperjerk system with a half line equilibrium. The mathematical framework of the proposed hyperjerk system contains eight terms with an absolute function nonlinearity. The essential dynamic characteristics of the model are explored, encompassing analysis of equilibrium points and their stability, depiction of the phase trajectories, illustration of bifurcation patterns, and visualization of Lyapunov exponent graphs. Our finding shows that the new 4D hyperjerk system exhibits special behavior like multistability, period doubling reversals and antimonotonocity. The proposed hyperjerk system has been implemented with an electronic circuit using MultiSim 14.0. Moreover, the FPGA implementation of the proposed hyperjerk system is performed by applying two numerical methods: Forward Euler and Trapezoidal. Experimental attractors are given from an oscilloscope by using the Zybo Z7-20 FPGA development board, which are in good agreement with the MATLAB and MultiSim 14.0 simulations. Finally, based on the chaotic dynamical behavior of the proposed chaotic hyperjerk system, a new image encryption approach is proposed. The experimental outcomes of the presented encryption algorithm prove its efficiency and security.

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Section: A New Hyperjerk System With a Half Line Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

Sambas,

Miroslav,

Vaidyanathan

et al. 2024

IEEE Access

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“…The proposed system is multiplier-less, variable boost, and entirely based on Chua diode nonlinearity. Karawanich et al [22] proposed a chaotic system based on the concept of third-order jerk. Zhang et al [23] developed a simple non-equilibrium chaotic system with only one sign function.…”

Section: Related Workmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chen,

Yu,

Luo

et al. 2024

Mathematics

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Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

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“…Following that, Rössler (1976), Rabinovich and Fabrikant (1979), and Chua et al (1993b) Cao and Zhao (2021). Only a few studies on circuit implementation of the chaotic system are based on OTA Karawanich and Prommee (2022); Yildirim (2022). The advantage of OTA over OPAMP component is its high output impedance, wide band gap, and transconductance gain which can be changed with bias current.…”

Section: Introductionmentioning

confidence: 99%

“…This provides an important advantage in chaotic circuits. The chaotic circuit design with OTA presented in Karawanich and Prommee (2022); Yildirim (2022) has been designed, but there is no study on its synchronization. In this study, a simpler structure is proposed by using only OTA, capacitor, and analog multiplier.…”

Section: Introductionmentioning

confidence: 99%

A Lorenz-like Chaotic OTA-C Circuit and Memristive Synchronization

AYDIN

BEKEN

Taşkıran

2023

Chaos Theory and Applications

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In this paper, a new set of lorenz-like hyper-chaotic equation set is obtained using the anti-control procedure. The chaoticity of the system is verified by MATLAB simulations using mathematical analysis methods. A new OTA-C circuit is designed for the new equation set. In the difference term addition technique, synchronizing the OTA-C circuit with a memristor rather than a resistor is proposed. Circuit design and synchronization are performed in PSpice simulation. The fact that the transresistance of the OTA element can be easily adjusted with a bias current provides the parameters that will make the proposed dynamic circuit a chaotic oscillator. The advantage of the proposed synchronization method is that the memristor automatically reaches to the value that will provide the required weight of the differential term required for synchronization, rather than the computational methods used to determine the weight.

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High-complex chaotic system based on new nonlinear function and OTA-based circuit realization

Cited by 14 publications

References 42 publications

A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

A Lorenz-like Chaotic OTA-C Circuit and Memristive Synchronization

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