A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu, Selçuk; Akgül, Akif; Adıyaman, Yusuf; Gümüş, Talha Enes; Uyaroğlu, Yılmaz; Yalçın, Mehmet Ali

doi:10.1108/cw-09-2020-0223

Cited by 11 publications

(7 citation statements)

References 34 publications

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“…This is a different approach that uses the fractional Lorenz equation set. Lately, there are popular studies on chaotic secure communication systems implemented by electronic components using active elements as op-amps [29], [30], current conveyor (CCII+) [31], [32], DVCCs [33] [34]. In May 1947, RAND corporation started creating random numbers by using an electronic simulation of a roulette wheel, and this study was published in 1955 as a random number book named A Million Random Digits with 100,000 Normal Deviates [35].…”

Section: Analysis and Applications Of A Hyperchaotic Systemmentioning

confidence: 99%

A novel analysis and applications of an introduced hyperchaotic system

Telli¹,

Taşkıran²

2022

Pamukkale J Eng Sci

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In this study, the new analysis of the introduced hyperchaotic equation set was handled. The equation set was firstly analyzed mathematically and then the results were proven by designing a more efficient circuit with active elements. The aim of the study is offering an effective secure communication application and random number generator application. Hence, based on the new analysis of equation set, secure communication system and random number generation application were proposed. Accordingly, creating a Pseudorandom Number Generator is the halfway house in this study. The signals received from the chaotic oscillator were sampled at low frequency and with a simple post-processing, a bit stream was created. The resulting bit stream passed the NIST test successfully. The other halfway of the study is creating a secure communication system by the synchronization of two chaotic oscillators that are in transmitter and receiver. An identical noise-like signals are generated in both transmitter and receiver parts. At the transmitter part adding a noise-like chaotic signal to the information is done. At the receiver, this same noise-like signal is subtracted from the perceived signal. Thus, the information can be transmitted securely. Spice simulations of both proposed applications have been made and it has been shown that they are compatible with mathematical analysis. The proposed circuits are suitable for realization with commercially available circuit elements.Bu çalışmada, tanıtılmış bir hiperkaotik denklem setinin yeni bir analizi ele alınmıştır. Denklem seti önce matematiksel olarak analiz edilmiş, ardından aktif elemanlarla daha verimli bir devre tasarlanarak sonuçlar kanıtlanmıştır. Çalışmanın amacı, etkili bir güvenli iletişim uygulaması ve rastgele sayı üreteci uygulaması sunmaktır. Bu nedenle, denklem setinin yeni analizi temel alınarak güvenli iletişim sistemi ve rastgele sayı üretme uygulaması önerilmiştir. Bu bağlamda, bir Sözde Rastgele Sayı Üreticisi oluşturmak, bu çalışmadaki yolun yarısıdır. Kaotik osilatörden alınan sinyaller düşük frekansta örneklenmiş ve basit bir post-processing ile bit dizileri oluşturulmuştur. Elde edilen bit dizisi NIST testinden başarı ile geçmiştir. Çalışmadaki yolun diğer yarısı ise verici ve alıcıda bulunan iki kaotik osilatörün senkronizasyonu ile güvenli bir iletişim sistemi oluşturmaktır. Hem verici hem de alıcı parçalarda özdeş bir gürültü benzeri sinyal üretilir. Verici kısmında bilgiye gürültü benzeri kaotik bir sinyal eklenmektedir. Alıcıda, bu aynı gürültü benzeri sinyal algılanan sinyalden çıkarılır. Böylece bilgiler güvenli bir şekilde iletilebilir. Önerilen iki uygulamanın da SPICE benzetimleri yapılmış, matematiksel analizler ile uyumlu olduğu gösterilmiştir. Önerilen devreler, ticari olarak bulunan devre elemanları ile gerçeklenmeye uygundur.

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Section: Analysis and Applications Of A Hyperchaotic Systemmentioning

confidence: 99%

A novel analysis and applications of an introduced hyperchaotic system

Telli¹,

Taşkıran²

2022

Pamukkale J Eng Sci

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“…Emiroglu et al [28] studied the problem of control of chaos in a ferroresonant circuit using backstepping nonlinear control to become stable in the equilibrium point and converge to the desired trajectory or point and demonstrated the effectiveness of designed control inputs for chaos control in ferroresonant phenomena. Then, Emiroglu et al [29] proposed a passive synchronization control method based on the new four-dimensional chaotic system to achieve the synchronization of the new four-dimensional chaotic system hyperchaotic system with different initial conditions. Alexander et al [30] designed a controller based on linear quadratic regulatory control and applied it to nonautonomous systems with infinite coexisting attractors, and the effectiveness of the controller was demonstrated through error.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

Ding,

Wang

2024

Advances in Mathematical Physics

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To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.

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“…The study of hyperchaotic systems was further developed in 1979 when Rössler discovered a four-dimensional hyperchaotic system [3]. Multidimensional chaotic and hyperchaotic systems became more well-known in the following years, providing useful applications in science and engineering [4]. Recently, there are many studies to be found in the literature on the dynamic analysis of chaotic systems [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers

Ozpolat,

Gulten

2024

Applied Sciences

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This paper explores the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this study, we introduce a novel hyperchaotic system, thoroughly examining its dynamic properties and conducting a comprehensive phase space analysis. The proposed hyperchaotic system undergoes validation through circuit simulation to confirm its behavior. Introducing an adaptive observer synchronization technique, we successfully synchronize the dynamics of the novel hyperchaotic system with an identical counterpart. Importantly, we extend the application of this synchronization method to the domain of secure communication, showcasing its practical usage. Simulation outcomes validate the effectiveness of our methodology, demonstrating favorable results in the realm of adaptive observer-based synchronization. This research contributes significantly to the understanding and application of hyperchaotic systems, offering insights into both the theoretical aspects and practical implementation. Our findings suggest potential advancements in the field of chaotic systems, particularly in their applications within secure communication systems. By presenting motivations, methods, results, conclusions and the significance of our work in a more appealing manner, we aim to engage readers and highlight the innovative contributions of this study.

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A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Cited by 11 publications

References 34 publications

A novel analysis and applications of an introduced hyperchaotic system

A novel analysis and applications of an introduced hyperchaotic system

Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking

Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers

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