Volume 4 (2013)  

Full text (PDF)

1.  Evidence of Noisy Chaotic Dynamics in the Returns of Four Dow Jones Stock Indices  Full text (PDF)

John Francis T. Diaz

Pages: 1-15

Abstract:  This research finds evidence of noisy chaotic properties in the returns of four Dow Jones indices, based on three tests of non-linearity and chaos. The study uses an average of 24,815 data points to correctly simulate chaos in financial time-series. The data consists of the Dow Jones Industrial Average (29,229 observations); Dow Jones Transportation Average (29,121 observations); Dow Jones Utility Average (21,150 observations) and the Dow Jones Composite Average (19,906 observations). The a) Brock, Dechert, and Scheinkman (BDS) test indicates that most of the Dow Jones indices are not iid series, except for the filtered residuals from the GARCH of the Dow Jones Utility Average. The b) rescaled range analysis shows that after scrambling the data, all Hurst exponents are above 0.5, and a trend-reinforcing property, which helps in the conclusion of having a chaotic process. Lastly, the c) correlation dimension analysis complements the initial findings and concludes the presence of a high dimensional noisy chaotic structure in the four Dow Jones indices.

2. Dynamic Behaviour of a Unified Two-Point Fourth Order Family of Iterative Methods Full text (PDF)

D. K. R. Babajee and S. K. Khratti

Pages: 15-29

Abstract:  Many variants of existing multipoint methods have been developed. Recently, Khratti et al. (2011) developed a unifying family of two-point fourth order methods which contains the well-known Ostrowski method. The authors also obtained some new methods which are variants of Ostrowskis method. However, it is difficult to compare the methods with the same of the order of convergence. The dynamic behaviour of the methods can be used as a tool for comparison. In this work, we study the dynamic of six members of the unifying family for some quadratic and cubic polynomials. By means of computer generated plots, we draw their polynomiographs for the polynomials f(z) = z21 and f(z) = z31 and explain their respective dynamic behaviour by analyzing the free critical and additional fixed points. Our results show that the methods exhibit different fractal behaviour and the most efficient method based on the size of its basins of attractions was found to the well-known Ostrowski method. This shows that these fourth order variants of Ostrowskis method are inefficient.

3. A Common Fixed Point Theorem of Presic Type for Three Maps in Fuzzy Metric Space  Full text (PDF)

P. P. Murthy, Rashmi  

Pages: 30-36

Abstract:  The present paper deals with a common fixed point theorem in Fuzzy metric space by implementing the concept of Presic fixed point theorem [16]. In this paper we have proved a unique common fixed point theorem of Presic type for three maps in a Fuzzy metric space. Also we have obtained the main theorem of R. George [Some fixed point results in dislocated fuzzy metric spaces, Journal of Advanced Studies in Topology, (2012), 3(4), 41-52] as a corollary by employing the conditions of our theorem for dislocated spaces.

4 Analysis of Dual Functions  Full text (PDF)

 Farid Messelmi

Pages: 37-55

Abstract:  The purpose of this paper is to develop a theory, inspired from complex analysis, of dual functions. In detail, we introduce the notion of holomorphic dual functions and we establish a general representation of holomorphic dual functions. As an application, we generalize some usual real functions to the dual plane. Finally, we will define the integral trough curves of any dual functions as well as the dual primitive.

5.  Chaotic Dynamical Behavior of Recurrent Neural Network Full text (PDF)

 A. Zerroug, L. Terrissa, A. Faure

Pages: 55-66

Abstract:  On account of their role played in the fundamental biological rhythms and by considering their potential use in information processing, the dynamical properties of an artificial neural network are particularly interesting to investigate. In order to reduce the degree of complexity of this work, we have considered in this paper a fully connected neural network of two discrete neurons. We have proceeded to a qualitative and quantitative study of their state evolution by means of numerical simulation. The first aim was to find the possible equilibrium states. Other authors have already shown that some oscillating state can occur. So, the second aim was to analyze the dynamical properties of each of them. We have computed the value of the Lyapunovs exponents and the fractal dimension. The sensitivity of the dynamical characteristics to parameters such as the weights of the connections nd the shape of the activation function has been studied.