Model equations from a chaotic time series

We present a method for obtaining a set of dynamical equations for a system that exhibits a chaotic time series. The time series data is first embedded in an appropriate phase space by using the improved time delay technique of Broomhead and King (1986). Next, assuming that the flow in this space is governed by a set of coupled first order nonlinear ordinary differential equations, a least squares fitting method is employed to derive values for the various unknown coefficients. The ability of the resulting model equations to reproduce global properties like the geometry of the attractor and Lyapunov exponents is demonstrated by treating the numerical solution of a single variable of the Lorenz and Rossler systems in the chaotic regime as the test time series. The equations are found to provide good short term prediction (a few cycle times) but display large errors over large prediction time. The source of this shortcoming and some possible improvements are discussed

Statistical Properties of Fluctuations: A Method to Check Market Behavior

We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal behavior of the returns using a recently developed wavelet based fluctuation analysis method. the returns show a fat-tail distribution as also weak non-statistical behavior. We have also carried out continuous wavelet as well as Fourier power spectral analysis to characterize the periodic nature and correlation properties of the time series.Comment: 9 pages, 6 figures, Econophys-IV, Kolkata, 200

A microscopic view of high-spin excitations in <SUP>90</SUP>Zr

The spectral structure of 90Zr has been studied by carrying out a configuration-mixing shell-model calculation in a deformed basis using Ip3/2, 0f5/2, 1p12/, 0g9/2 model space. A modified Kuo-Brown effective interaction has been used. The band structure for the positive- and negative-parity states has been inferred through enhanced intraband E2 transitions as compared with the weak interband transitions. The present calculation describes fairly well the observed positive-parity states including the odd-J states as well as the negative-parity states. Many high-spin states and intraband E2 transition strengths have been predicted

Coexistence of shapes and the role of the g<SUB>9/2</SUB> orbit in Se isotopes

The phenomenon of the coexistence of nuclear shapes in <SUP>70,72,74</SUP>Se is studied within the framework of the deformed configuration mixing shell model. In this model, <SUP>56</SUP>Ni is taken as the core with the valence space consisting of 1p<SUB>3/2</SUB>, 1p<SUB>1/2</SUB>, 0f<SUB>5/2</SUB> and 0g<SUB>9/2</SUB> orbitals. An effective interaction given to Kuo and modified by Ahalpara and others has been used. The crossing of a nearly spherical ground state band and a highly deformed band in <SUP>70,72</SUP>Se are given by the calculation in agreement with experiment. The calculation does not show any such band crossing in <SUP>74</SUP>Se. The role of the g<SUB>9/2</SUB> orbital in producing highly deformed two neutron aligned bands is stressed

Collective band structure in <SUP>66</SUP>Zn

The collective nature of states in <SUP>66</SUP>Zn has been studied by carrying out a deformed configuration mixing shell model calculation in (1p<SUB>3/2</SUB>0f<SUB>5/2</SUB>1p<SUB>1/2</SUB>0g<SUB>9/2</SUB>) model space. An effective interaction obtained for this space by Kuo has been used. The collective structure for 2 positive-parity bands and 5 negative-parity bands is identified. A qualitative understanding of the backbending at the J=6<SUP>+</SUP> state in the yrast positive-parity band is given in terms of the band crossing of the ground-state band and the more deformed excited band arising from 2p2h excitation to the g<SUB>9/2</SUB> orbit. Several high-spin members of the observed bands as well as in-band E2 transition strengths have been predicted