Tent map

About: Tent map is a research topic. Over the lifetime, 623 publications have been published within this topic receiving 6834 citations.

Chaotic whale optimization algorithm

Abstract: The Whale Optimization Algorithm (WOA) is a recently developed meta-heuristic optimization algorithm which is based on the hunting mechanism of humpback whales. Similarly to other meta-heuristic algorithms, the main problem faced by WOA is slow convergence speed. So to enhance the global convergence speed and to get better performance, this paper introduces chaos theory into WOA optimization process. Various chaotic maps are considered in the proposed chaotic WOA (CWOA) methods for tuning the main parameter of WOA which helps in controlling exploration and exploitation. The proposed CWOA methods are benchmarked on twenty well-known test functions. The results prove that the chaotic maps (especially Tent map) are able to improve the performance of WOA.

An image encryption scheme based on chaotic tent map

Abstract: Image encryption has been an attractive research field in recent years. The chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a novel image encryption scheme, which is based on the chaotic tent map. Image encryption systems based on such map show some better performances. Firstly, the chaotic tent map is modified to generate chaotic key stream that is more suitable for image encryption. Secondly, the chaos-based key stream is generated by a 1-D chaotic tent map, which has a better performance in terms of randomness properties and security level. The performance and security analysis of the proposed image encryption scheme is performed using well-known ways. The results of the fail-safe analysis are inspiring, and it can be concluded that the proposed scheme is efficient and secure.

A secret key cryptosystem by iterating a chaotic map

Abstract: Chaos is introduced to cryptology. As an example of the applications, a secret key cryptosystem by iterating a one dimensional chaotic map is proposed. This system is based on the characteristics of chaos, which are sensitivity of parameters, sensitivity of initial points, and randomness of sequences obtained by iterating a chaotic map. A ciphertext is obtained by the iteration of a inverse chaotic map from an initial point, which denotes a plaintext. If the times of the iteration is large enough, the randomness of the encryption and the decryption function is so large that attackers cannot break this cryptosystem by statistic characteristics. In addition to the security of the statistical point, even if the cryptosystem is composed by a tent map, which is one of the simplest chaotic maps, setting a finite computation size avoids a ciphertext only attack. The most attractive point of the cryptosystem is that the cryptosystem is composed by only iterating a simple calculations though the information rate of the cryptosystem is about 0.5.

Generalized dimensions and entropies from a measured time series.

Abstract: The correlation-integral method of Grassberger and Procaccia is generalized to yield the whole spectrum of dimensions ${D}_{q}$ and entropies ${K}_{q}$ from a measured time series with a numerical effort which is only insignificantly larger than that needed to determine the original correlation integral. It is shown that our method yields reliable numerical results for the tent map and for the Mackey-Glass equation.

Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Abstract: Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.