Right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis

Wu, Guo–Cheng; Wei, Jia-Li; Luo, Maokang

doi:10.1080/10236198.2023.2198043

Cited by 10 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is popular to study the discrete-time version from the time-scale theory [6]. In fact, some applications and theories were considered in the power-law definition [1,2,4], discrete-time fractional variational problems [5,8], fractional chaotic maps [17,21,24], fractional recurrent neural network [14], Hadamard difference [20,23] and finite-time stability [18,22]. In view of these results, the new features and main reasons why we investigate discrete fractional calculus are the following:…”

Section: Introductionmentioning

confidence: 99%

Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability

Yang,

Wu,

2023

NAMC

View full text Add to dashboard Cite

A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.

show abstract

Section: Introductionmentioning

confidence: 99%

Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability

Yang,

Wu,

2023

NAMC

View full text Add to dashboard Cite

show abstract

Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation

Beyene,

Rahma,

Rajagopal

et al. 2023

J Nonlinear Math Phys

View full text Add to dashboard Cite

This article, a 3D fractional-order chaotic system (FOCS) is designed; system holds Equilibria can take on various shapes and forms by introducing a nonlinear function and the value of its parameters. To comprehend the system’s behavior under diverse conditions and parameter values, a dynamical analysis is conducted through analytical and numerical means. This analysis employs techniques like phase portraits, Lyapunov exponents (LEs), bifurcation analysis, and Lyapunov spectra. The system demonstrates attractors that are more intricate compared to a regular chaotic system with an integer value, specifically if we set the fractional order q to 0.97. This characteristic makes it highly appropriate for developing secure communication systems. Moreover, a practical implementation has been developed using an electronic circuit to showcase its feasibility of the system. A secure communication system was built using two levels of encryption techniques. The propose sound encryption algorithm is verified through tests like histogram, correlation, and spectrogram investigation. The encryption correlation coefficient between the original signal and the encrypted one is 0.0010, this result shows a strong defences against pirate attacks.

show abstract

On fractional ring neural networks with multiple time delays: Stability and Hopf bifurcation analysis

Hou,

Luo,

2024

Chinese Journal of Physics

View full text Add to dashboard Cite

Right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis

Cited by 10 publications

References 29 publications

Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability

Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability

Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation

On fractional ring neural networks with multiple time delays: Stability and Hopf bifurcation analysis

Contact Info

Product

Resources

About