Logistic Map Equation Research Articles

Study of decay rate of materials using logistic map equation

The bifurcation diagram obtained till date is for population dynamics given by Robert May and analyzed and plotted for many relative graphs by Feigenbaum with emergence of Feigenbaum constant. Author here tried to apply the same logistic equation with negative growth rate, can be called as decay rate which can relate to decomposition processes in nature or materials. The universality of the bifurcation diagram and the Feigenbaum constant is also proved in this region. The decay rate hence obtained has a different values than that of existing growth rate values.

Fuzzy Logic Based Time Series Prediction Algorithm Using Nearest Neighborhood Clustering

This paper presents a fuzzy logic based prediction algorithm using nearest neigh-borhood clustering for the prediction of time series. The proposed algorithm hasbeen developed by using nearest neighborhood clustering scheme and optimalfuzzy system. The presented algorithm is tested by the prediction of Mackey-Glass time series, time series obtained from Logistic Map equation and an oilrefinery data series. To the best of our knowledge very few studies have at-tempted to predict Logistic Map. The results of the experimentation show thatthe presented prediction algorithm is able to predict linear, nonlinear and evenchaotic time series to a reasonable accuracy. It performes well even when themathematical model of time series does not exist.

Fused Iris Biometric Template Formation Using Logistic Maps and LFSR

Biometrics is a technology that is currently being used in diverse aspects of life for hassle free authentication and verification. Biometric finds itself in almost every critical infrastructure secure access systems thus stepping on as a surrogate representation of an individual. The flip side to this surrogate representation is that if its compromised, it implies an identity theft of an individual. To circumvent this issue of identity theft in general and biometric template security in particular, we propose and implement a new fused biometric iris encryption algorithm for the generation of a secure biometric iris template. The proposed algorithm uses two separate keys: one derived from a logistic map equation and other from the linear feedback shift register. The two keys encrypt left iris and right iris images separately, thus giving an left encrypted image and right encrypted image. The two encrypted images are fused to get a final template to be stored. In order to evaluate and analyse the performance, the proposed algorithm was put through a cascade of tests: subjective and objective. Result analysis show that depict that key space is significantly enhanced in the proposed work. Also the proposed crypto-system shows good sensitivity to any change in the key.

Chaos-Modified Lightweight Present Algorithm for Image Encryption

At the present time, the increase of data transmission over various networks in a wide range, which led to the need for a high level of security. One of the most important methods that have been invented to protect and integrity data is encryption. This paper test the efficiency of an algorithm for image encryption that utilizes a Lightweight present algorithm whit a chaotic logistic map equation. Where we relied on the chaos to produce the keys that were used in the proposed algorithm. Through the results, we observed that the modified algorithm is faster and safer. Also, the correlation neighboring pixels is about 0; no relationship at all between the two image versions. , the proposed algorithm gets better the encryption efficiency compared The original algorithm

Observation of Different Behaviors of Logistic Map for Different Control Parameters

The logistic map is one of the most important but common examples of chaotic dynamics. The object shows the crucial belief of the deterministic chaos theory that brings a new procedural structure and apparatus for exploring and understanding complex behavior in dynamical systems. We put an importance on report of the Verhulst logistic map which is one of the potential models and methods for researching dynamical systems that could develop to chaotic. Chaotic signals present a special difficulty in parameter estimation. The difficulty arises from the definition of a chaotic system because of sensitive dependence on initial conditions. It is seen that very slight changes in the initial conditions cause significant effects in the evolution. In general the chaotic systems are nonlinear and apparently random but they are deterministic. The main objective of this paper is how can find the logistic map equation and investigated the chaotic behavior for the logistic equation by varying the control parameters and finally discover Lyaponov exponent, Bifurcation diagrams etc.

Developing a chaotic pattern of dynamic risk definition for solving hazardous material routing-locating problem

In the case of determining routes and locations for constructing distribution centers on hazardous materials (Hazmat) transportation, risk and cost are considered as the main attributes for developing mathematical models. Since, Hazmat transport risk may be defined as a chaotic factor, using dynamic risk changes the selected routes and optimized locations for constructing distribution centers.In the present paper, an iterative procedure has been proposed to determine the best routes and optimized locations of distribution centers for transporting hazardous materials based on the concept of chaos theory in which hazmat transport risk is defined as a dynamic variable. A mathematical model has been developed for solving Hazmat routing and locating problems, simultaneously. Daily transport risk, defined as a chaotic variable, is iteratively updated using one-dimensional logistic map equation over the time period (year). An experimental road network, consists of eighty nine nodes and one hundred and three two-way edges, has been selected for analytical process and model validation. Results revealed that although different amounts of risk and cost priorities change optimized locations of distribution centers and their associated supplies, but the most frequent set of optimized centers remains independent. Therefore, the proposed procedure is capable to determine the best routes and optimized locations for distributing hazardous materials. While risk is iteratively updated over a specific time period, results show that the main property of chaos theory known as dependency upon initial condition would not be a serious concern for decision makers who are dealing with Hazmat management.

Two Chaotic Patterns of Dynamic Risk Definition for Solving Hazardous Materials Routing Problem

In the case of determining routes for hazardous material transportation, risk is considered as a main attribute. Transport risk, which is usually combined with other attributes such as cost or travel time, plays a significant role in determining paths for hazardous materials transportation. Since, risk is chaotically affected by road incidents, decision makers are dealing with selecting a method for defining chaotic risk factors in hazmat transportation. In this paper, transport risk has been defined as a chaotic variable using two different methods of generating chaotic patterns. In an experimental road network, which consists of eighty-nine nodes and one hundred and one two-way links, two different methods of generating chaotic variables have been used for applying the proposed procedure. In addition, results for different amounts of risk and cost have also been analyzed in case study. Results revealed that different cost and risk priorities change the frequencies of selected paths determined for hazmat transportation, but the route convergence of the route to chaos method is better than that of the logistic map equation.

Which Pure Chaos Model Will Describe IDX Composite (Jakarta Composite Index (JCI) of Indonesia Stock Exchange (IDX)) Better?

Is it possible to approach a time series by modeling it through a predicted model of a fully deterministic and pure chaotic model? IDX Composite (Jakarta Composite Index) time series will be examined whether it can be explained by one of renowned fully deterministic and pure chaotic models or their variants.Daily return data of Jakarta Composite Index (JCI) of Indonesia Stock Exchange from January 05, 1988 to June 30, 2009 are observed. “Compass rose” pattern of scatter diagram will be observed. Chosen renowned fully deterministic and pure chaotic models are Logistic map equation, Henon map and Mackey Glass delay differential equation which have low dimensionality. The initial value return of JCI is applied to three chaotic models to create the chaotic series that have the same initial conditions with JCI return. The length of data points of chaotic series is set to be the same length of JCI series.In addition to the scatter diagram comparisons other three tests are applied to all chosen chaos models and JCI series. BDS Statistic, R/S Analysis and Lyapunov Exponent of Wolf et al (1985) algorithm are the used test tools to investigating some characteristics of chaotic system: nonlinear, persistence (fractal) and sensitive dependence on initial condition. Performance results of chaos characteristic tests on chosen models will be explored to approach predicted chaotic model of JCI. The objective of this research result is to find - if any - the best approached and fitted chaos model to describe JCI better as an approximation model. Understanding of chaotic attributes - nonlinear, fractal and sensitive dependence on initial condition - will provide better analysis of non periodicity of crisis on Indonesia Stock Exchange as well as of phenomenon of crisis, order and disorder on Indonesia Stock Exchange.