Extreme multistability arising from periodic repetitive bifurcation behavior in a hyperchaotic oscillator

Wang, Xuan; Mou, Jun; Jahanshahi, Hadi; Alotaibi, Naif D.; Bi, Xiuguo

doi:10.1007/s11071-023-08562-z

Cited by 19 publications

(5 citation statements)

References 46 publications

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“…The circuit consists of a meminductor LM, a memcapacitor CM, a resistor R, a negative resistor G and a capacitor C. The circuit schematic diagram of the hyperchaotic oscillator is shown in Figure 1. The equation for the state of the circuit can be expressed as [38]:…”

Section: Numerical Solution For Fommsmentioning

confidence: 99%

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A Chaos-Enhanced Fractional-Order Chaotic System with Self-Reproduction Based on a Memcapacitor and Meminductor

Wang,

Cao,

et al. 2023

Fractal Fract

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Chaotic signals generated by chaotic oscillators based on memory elements are suitable for use in the field of confidential communications because of their very good randomness. But often their maximum Lyapunov exponent is not high enough, so the degree of randomness is not enough. It can be chaos enhanced by transforming it to fractional order using the Caputo differential definition. In this paper, based on the proposed hyperchaotic oscillator, it is extended to a fractional-order form to obtain a chaos-enhanced fractional-order memcapacitor meminductor system, in which several different styles of chaotic and hyperchaotic attractors are found. The dynamical behaviour of the system is studied using bifurcation diagrams, Lyapunov exponent spectrums and Lyapunov dimensions. The multistability of the system is explored in different initial orbits, and the spectral entropy complexity of this system is examined. Finally, a hardware implementation of the memcapacitor meminductor system is given, which demonstrates the effectiveness of the system. This study provides a reference for the study of chaos-enhanced.

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Section: Numerical Solution For Fommsmentioning

confidence: 99%

“…By introducing the Caputo differential definition, the fractional order form of the dimensionless equation for the above circuit can be written: The equation for the state of the circuit can be expressed as [38]:…”

Section: Numerical Solution For Fommsmentioning

confidence: 99%

A Chaos-Enhanced Fractional-Order Chaotic System with Self-Reproduction Based on a Memcapacitor and Meminductor

Wang,

Cao,

et al. 2023

Fractal Fract

Self Cite

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“…[25] Because constructing nonlin-ear circuits through memory elements is an important research direction of chaotic systems, the selected system is of great practical significance. [26,27,56,[58][59][60] For the dispute of copyright ownership, scholars regard watermark technology as the first choice to solve the problem. [28] The perfection and diversification of watermarking technology make scholars see its huge application value and classify it according to its functions, such as zero watermarking, robust watermarking, laser watermarking, frequency domain watermarking and so on.…”

Section: Introductionmentioning

confidence: 99%

Novel self-embedding holographic watermarking image encryption protection scheme

Wang 王,

Zhou 周,

Sun 孙

et al. 2024

Chinese Phys. B

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For digital image transmission security and information copyright, a new holographic image self-embedding watermarking encryption scheme is proposed. Firstly, the plaintext is converted to the RGB three-color channel, the corresponding phase hologram is obtained by holographic technology and the watermark is self-embedded in the frequency domain. Secondly, by applying Hilbert transform principle and genetic center law, a complete set of image encryption algorithm is constructed to realize the encryption of image information. Finally, simulation results and security analysis indicate that the scheme can effectively encrypt and decrypt image information and realize the copyright protection of information. The introduced scheme can provide some support for relevant theoretical research, and therefore has practical significance.

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“…To find the solitary waves and soliton solutions of nonlinear partial differential equations (NLPDEs), there is a wide range of analytical and numerical techniques. These techniques include the Darboux transformation [4,5], the Backlund transformation [6], the extended trial equation method [7], the first integral method [8], the modified simple equation method [9], the Riccati-sub-ODE Bernoulli method [10], the generalized exponential rational functions method [11], chaotic behavior and bifurcation analysis [12,13], the Jacobi elliptical expansion method [14], the extended F-expansion method [15], the sine-gordan expansion method [16,17], the new extended direct algebraic method [18], and lump soliton solution [19,20], many other similar methods have also been extended in this field [21].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of optical solitons and sensitivity analysis in fiber optics

Raees,

Mahmood,

Hussain

et al. 2024

Preprint

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The nonlinear Schrödinger equation (NLSE) and its various forms have significant applications in the field of soliton theory. The Fokas-Lenells (FL) equation stands as a cornerstone in deepening our understanding of nonlinear wave dynamics within optical systems, particularly concerning the behavior of ultrashort pulses across different media. Its significance lies in providing a comprehensive framework to study and analyze complex phenomena, ultimately contributing to advancements in optical technology and applications. The FL equation is an integrable extension of the NLSE that provides a description of the nonlinear propagation of pulses in optical fiber. This paper seeks to discover optical soliton solutions for the FL equation by employing a modified sub-equation method. Additionally, the sensitivity analysis is described by using the various initial conditions. For the physical behavior of the models, some solutions are graphically shown in 2D, 3D and contour graphs by assigning specific values to the parameters under the provided situation at each solution. As a result, we discovered several new families of exact traveling wave solutions, such as bright solitons, dark solitons, and combined bright and dark soliton. As a result, investigated solutions have significant advantages in the field of mathematical physics. Mathematics subject classification (2020) : 39A1; 39B62; 33B10; 26A48; 26A51

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Extreme multistability arising from periodic repetitive bifurcation behavior in a hyperchaotic oscillator

Cited by 19 publications

References 46 publications

A Chaos-Enhanced Fractional-Order Chaotic System with Self-Reproduction Based on a Memcapacitor and Meminductor

A Chaos-Enhanced Fractional-Order Chaotic System with Self-Reproduction Based on a Memcapacitor and Meminductor

Novel self-embedding holographic watermarking image encryption protection scheme

Dynamics of optical solitons and sensitivity analysis in fiber optics

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