In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems. Chaotic maps and iterated functions often ...

A chaotic map is a cryptosystem that utilizes nonlinear functions to create complex random sequences for encrypting data. The output of chaotic maps is heavily influenced by control parameters and initial settings, making them effective tools for cryptography. AI generated definition based on: Advances in Computers, 2023.

The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side onto itself. [1] It is constructed by a Poincaré's surface of section of the kicked rotator , and is defined by:

In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name. [1] It is a simple and pedagogical example for hyperbolic toral automorphisms.

Mar 25, 2015 · The logistic map instead uses a nonlinear difference equation to look at discrete time steps. It’s called the logistic map because it maps the population value at any time step to its value at the next time step: $latex x_{t+1} = r x_t (1-x_t)$

Jan 18, 2022 · Chaotic maps are mathematical functions that generate a highly arbitrary pattern based on the initial seed value. This manuscript gives a summary of how the chaotic maps are used to generate pseudo-random numbers and perform multimedia encryption.

This paper proposes a robust optimization of eight chaotic maps: Logistics, Sine, Gauss, Circle, Tent, Chebyshev, Singer, and Piecewise Maps, for superior image encryption.

In discussing chaotic dynamical systems, interval maps provide examples that can be easily visualized. Two standard examples are the full tent map x 7→ 1−|1−2x|, and the conjugate map x 7→4x(1−x). A logistic map f k(x) = kx(1−x) for k > 4 is also chaotic, if restricted to the set X of points in [0,1] whose orbits stay in [0,1], cf. [6].

Example Chaotic Maps (that you can analyze) Reading for this lecture: NDAC, Sections10.5-10.7. Lecture 7: Nonlinear Physics, Physics 150/250 (Spring 2010); Jim Crutchfield Monday, May 17, 2010 1

Chaotic systems have long played a crucial role in cryptographic applications due to their inherent unpredictability and sensitivity to initial conditions. Building on this foundation, this paper introduces an Improved Composite Chaotic Map (ICCM), inspired by classical quadratic and cubic chaotic maps. The proposed ICCM is rigorously validated …