Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers

Natiq, Hayder; Banerjee, Santo; Misra, A. P.

doi:10.1016/j.chaos.2019.03.009

Cited by 40 publications

(17 citation statements)

References 28 publications

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“…Zang et al [28] constructed a 4D hidden chaotic attractor with extreme multistability behaviors by introducing a feedback controller on a 3D autonomous chaotic system. Natiq et al [29] introduced two nonlinear controllers on a 3D chaotic system to generate coexistence of two or four chaotic attractors. Some examples of the second type are as follows.…”

Section: Introductionmentioning

confidence: 99%

A New S-Box Generation Algorithm Based on Multistability Behavior of a Plasma Perturbation Model

et al. 2019

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This paper investigates the dynamics of a 3D plasma system that has a single symmetric double-wing attractor moving around symmetric equilibria. Therefore, it is reasonable to assume that changing the space between these wings can degenerate them. Motivated by this concept, we introduce a new controller on the plasma system that can shift its equilibria away from each other, and subsequently break the symmetric double-wing that resembles a butterfly into several independent chaotic attractors. To show the advantage of generating coexisting attractors, we compare between the complexity performance of the multi-stable controlled plasma system and the original plasma system that has single chaotic attractor. Simulation results show that the complexity performance of the multi-stable controlled plasma system is higher than the original system. As a result, and from cryptographic point of view, chaotic ciphers with applying more than one set of initial conditions provide a higher level of security than applying only one set of initial conditions. As an example, we present a new approach for generating S-box based on the multistability behavior of the controlled plasma system. Performance analysis shows that the proposed S-box algorithm can achieve a higher security level and has a better performance than some of the latest algorithms.INDEX TERMS Equilibria, stability, coexisting attractors, fuzzy entropy, chaos-based cryptography.ALAA KADHIM FARHAN received the bachelor's degree in computer science, and the M.Sc. and Ph.D. degrees in information security from the

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Section: Introductionmentioning

confidence: 99%

A New S-Box Generation Algorithm Based on Multistability Behavior of a Plasma Perturbation Model

et al. 2019

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“…is nonlinear behavior is termed as coexisting attractors or multistability. Multistability behaviors [11,12] of the physical system act as important feature in the dynamics of nonlinear systems. Experimentally, multistability feature was firstly investigated in a Q-switched gas laser [13]; thereafter, various works [14,15] were reported in different complex systems exhibiting multistability features.…”

Section: Introductionmentioning

confidence: 99%

“…Probable phase plots of the dynamical system(12) for κ � 5, n b0 � 0.01, n e0 � 0.99, n i0 � 0.05, n p0 � 0.9, σ b � 0.0025, σ i � 0.4, σ p � 0.2, V bo � 17.14, μ pb � 1836, and μ pi � 0.25187 with (a) V � 1.1, (b) V � 1.225, (c) V � 1.24, and (d) V � 1.3.…”

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Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Prasad

Mukherjee²,

Saha

et al. 2020

Complexity

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Dynamical complexity and multistability of electrostatic waves are investigated in a four-component homogeneous and magnetized lunar wake plasma constituting of beam electrons, heavier ions (alpha particles, He ++ ), protons, and suprathermal electrons. e unperturbed dynamical system of the considered lunar wake plasma supports nonlinear and supernonlinear trajectories which correspond to nonlinear and supernonlinear electrostatic waves. On the contrary, the perturbed dynamical system of lunar wake plasma shows different types of coexisting attractors including periodic, quasiperiodic, and chaotic, investigated by phase plots and Lyapunov exponents. To confirm chaotic and nonchaotic dynamics in the perturbed lunar wake plasma, 0 − 1 chaos test is performed. Furthermore, a weighted recurrence-based entropy is implemented to investigate the dynamical complexity of the system. Numerical results show existence of chaos with variation of complexity in the perturbed dynamics.

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“…In the past few decades, Tokamak plasma physics has been widely studied in various research fields such as physical experiment research and engineering technology applications. Especially, the dynamical behaviors of interaction between drive and relaxation processes in a deterministic or perturbed toroidal Tokamaks magnetic field have been investigated by many scholars [5,6,7].…”

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confidence: 99%

“…with η = 2χ 0 /(γ 0 al grad ) and h = H tot /(4π 2 Rap crit χ 0 ). In short, the plasma perturbation model consists of the equation 3and (5) with respect to the amplitude of the magnetic field displacement ξ n and the plasma pressure gradient p n , which contains only three parameters: the power input h, the relaxation of the instability δ, the influence of the instability on the heat diffusion coefficient η.…”

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Complex dynamics in a quasi-periodic plasma perturbations model

Zhang¹,

Yang²

2021

DCDS-B

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In this paper, the complex dynamics of a quasi-periodic plasma perturbations (QPP) model, which governs the interplay between a driver associated with pressure gradient and relaxation of instability due to magnetic field perturbations in Tokamaks, are studied. The model consists of three coupled ordinary differential equations (ODEs) and contains three parameters. This paper consists of three parts: (1) We study the stability and bifurcations of the QPP model, which gives the theoretical interpretation of various types of oscillations observed in [Phys. Plasmas, 18(2011):1-7]. In particular, assuming that there exists a finite time lag τ between the plasma pressure gradient and the speed of the magnetic field, we also study the delay effect in the QPP model from the point of view of Hopf bifurcation. (2) We provide some numerical indices for identifying chaotic properties of the QPP system, which shows that the QPP model has chaotic behaviors for a wide range of parameters. Then we prove that the QPP model is not rationally integrable in an extended Liouville sense for almost all parameter values, which may help us distinguish values of parameters for which the QPP model is integrable. (3) To understand the asymptotic behavior of the orbits for the QPP model, we also provide a complete description of its dynamical behavior at infinity by the Poincaré compactification method. Our results show that the input power h and the relaxation of the instability δ do not affect the global dynamics at infinity of the QPP model and the heat diffusion coefficient η just yield quantitative, but not qualitative changes for the global dynamics at infinity of the QPP model.

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Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers

Cited by 40 publications

References 28 publications

A New S-Box Generation Algorithm Based on Multistability Behavior of a Plasma Perturbation Model

A New S-Box Generation Algorithm Based on Multistability Behavior of a Plasma Perturbation Model

Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Complex dynamics in a quasi-periodic plasma perturbations model

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