A new experimental approach to study the stability of logistic map

Improving Security of the Baptista's Cryptosystem Using Two-step Logistic Map

“…In 2009, Rani and Agarwal [11] gave a new study of the stability of logistic map, in which they enhanced the capabilities of logistic map via superior iterations. It is a two-step feedback mechanism in which new iterated value of x is calculated using previous two values of x with factor B∈ (0, 1] as (4).…”

“…So in the proposed scheme, we shall use a two-step logistic map to enhance the capabilities of chaotic cryptosystem. [11] as (5) and (6) first for encrypting data and second for updating the lookup table.…”

Stability and Fractal Patterns of Complex Logistic Map

“…A two step feedback scheme requiring two numbers as input to return a new number as output is used by R a n i and A g a r w a l [26] for the study of the chaotic behaviours of the logistic map. The n-th, n = 1, 2, 3, …, iterate of this is given as x n = α n f(x n-1 ) + (1-α n ) x n-1 , where 0 < α n ≤ 1 and the sequence {α n } is converging away from 0.…”

“…Due to the advancement of modern computational tools and proliferation of digital computers, new vistas have been opened for the study and analysis of these hyper sensitive maps and the literature is flourished with the papers signifying their importance in chaos, fractals, cryptography, optimization, discrete dynamics, population dynamics etc. (see for instance, [5,6,11,17,18,19,21,22,26,28] and several references thereof). K i n t et al [13] explored the graphical potential of this map and generated fractal figures comparable to the well known Mandelbrot fractals.…”

On the Convergence of Logistic Map in NOOR Orbit

“…In 2005, Rani and Kumar [20] studied logistic map via new approach. They introduced the superior orbit as an example of two-step iterative procedure and showed that the logistic map is convergent for the large value of "r" as compared to Picard orbit.…”