A new perturbation method to the Tent map and its application

Abstract

Disturbance imposed on the chaotic systems is an effective way to maintain its chaotic good encryption features. This paper proposes a new perturbation method to the Tent map. First it divides the Tent map domain into 2 N parts evenly and selects a particular part from them, then proliferates the Tent map mapping trajectory of this particular part, which can disturb the entire system disturbance. The mathematical analysis and simulated experimental results prove that the disturbed Tent map has uniform invariant distribution and can produce good cryptographic properties of pseudo-random sequence. These facts avoid the phenomenon of short-period caused by the computer's finite precision and reducing the sequence's dependence on the disturbance signal, such that effectively compensate for the digital chaotic system dynamics degradation.

A precise inversion method of cable joint core temperature with non-embedded detection based on UMAP and ISSA-BPNN

“…However, the probability of logistic mapping in the interval of [0,0.1] and [0.9,1] is much higher than the probability of the middle position (Zhang and Ding, 2021). By contrast, the Tent chaos mapping in the interval of [0,1] has better ergodicity and uniformity (Wang and Wang, 2011;Liu et al, 2022c). In addition, in order to overcome the shortcomings of traditional Tent chaotic mapping and avoid chaotic particles falling into the small period and unstable period points during iteration, a random variable rand(0,1)/N is added to the original mapping formula, and the modified Tent chaotic mapping can be expressed as follows:…”

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

“…The dimensionless oil film damping is µ o = cηP 14 11 m /Ω 24 11 , where c is constant. Thus, the dimensionless system model can be expressed as…”

“…Bifurcation and chaos are important parts of the nonlinear scientific fields. [7][8][9][10] They have achieved rapid development and extensive applications in the fields of secure communications [11][12][13] and signal processing. [14][15][16] At the same time, the Hopf bifurcation was analyzed on the basis of the relative rotation theory, and the nonlinear and nonlinear time-delayed feedback control techniques were proposed to control the bifurcation points and the stability of periodic solutions.…”

Counteracting dynamical degradation of a class of digital chaotic systems via Unscented Kalman Filter and perturbation

“…(e) The perturbation method (e.g. in the approaches of [28,29,30,31,32,33]), which is a common method and is easy to implement on a digital platform. The perturbed objects include inputs, outputs, and parameters of the chaotic systems, and when the feedback-control algorithm is well designed, the perturbation method can effectively ameliorate the dynamical degradation of the digital chaotic systems without large-scale computing and system integration, which makes it universally applicable to chaos-based cryptosystems and communication [28].…”