Chaotic Behavior Of Logistic Map Research Articles

Chaotic behavior of logistic map in superior orbit and an improved chaos-based traffic control model

With a vital role of discrete chaos, standard logistic map has found a celebrated place in the dynamics of chaos theory and in various applications of science, such as a discrete traffic flow model, image encryption in cryptography, secure communication, and weather forecasting. Traditionally, this discrete chaos is controlled by one parameter $$\lambda $$ using Picard orbit, a one-step feedback procedure. This article presents a one-step forward, applying Mann orbit (superior orbit) the chaotic properties such as period-doubling, period-3 window, and Lyapunov exponent of the standard logistic map is investigated. The results are illustrated analytically and experimentally followed by concluding remarks and a few counter examples. Due to the extra degree of freedom in parameter $$\lambda $$ , the map provides improved chaotic properties that increases the performance of dynamical phenomena. Moreover, this study describes an improved chaos-based discrete traffic control model. Surprisingly, added new parameter $$\alpha $$ in Mann orbit works as control variable that increases the stability performance of the traffic model.

Biometric Template Protection Using Spiral Cube: Performance and Security Analysis

Personal authentication systems based on biometrics have given rise to new problems and challenges related to the protection of personal data, issues of less concern in traditional authentication systems. The irrevocability of biometric templates makes biometric systems very vulnerable to several attacks. In this paper we present a new approach for biometric template protection. Our objective is to build a non-invertible transformation, based on random projection, which meets the requirements of revocability, diversity, security and performance. In this context, we use the chaotic behavior of logistic map to build the projection vectors using a methodology that makes the construction of the projection matrix depend on the biometric template and its identity. The proposed approach has been evaluated and compared with Biohashing and BioPhasor using a rigorous security analysis. Our extensive experimental results using several databases (e.g., face, finger-knuckle and iris), show that the proposed technique has the ability to preserve and increase the performance of protected systems. Moreover, it is demonstrated that the security of the proposed approach is sufficiently robust to possible attacks keeping an acceptable balance between discrimination, diversity and non-invertibility.

A new experimental approach to study the stability of logistic map

Remarkably benign looking logistic transformations x n + 1 = rx n (1 − x n ) for choosing x 0 between 0 and 1 and 0 < r ⩽ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The purpose of this paper is to enhance the capabilities of logistic map via superior iterations. Stability of logistic map has been studied by running computer programs. Logistic map is stable for 0 < r ⩽ 3.2 in Picard orbit. In superior orbit, we see that the range of stability of logistic map increases drastically. Also, chaotic behavior of logistic map disappears in certain cases.

Complexities and Their Applications to Characterization of Chaos

The concept of complexity in InformationDynamics is discussed. The chaos degree defined by thecomplexities is applied to examine chaotic behavior oflogistic map.