Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Compact asymmetric coplanar waveguide filter

The design and implementation of a novel asymmetric coplanar waveguide (ACPW ) band rejection filter using defected ground structure ( DGS) is presented . The proposed ACPW DGS technology provides band gap characteristics with only one cell in the lateral ground plane . The equivalent circuit model of the proposed DGS unit section is described . Measurements of ACPW DGS showed good agreement with simulation and the proposed model

A Wideband Rectangular Microstrip Antenna Using an Asymmetric t-shaped Feed

An electromagnetically coupled T-shaped microstrip feed used to enhance the impedance bandwidth of a rectangular microstrip antenna is reported. The proposed antenna offers a 2:1 VSWR bandwidth of -36% with an increase in gain of 0.8 dB

DESIGN AND DEVELOPMENT OF COMPACT ASYMMETRIC COPLANAR STRIP FED ANTENNAS

Antennas are indispensable component of any wireless communication device. An antenna is a transducer between the transmitter and the free space waves and vice versa. They efficiently transfer electromagnetic energy from a transmission line into free space. But the present day communication applications require compact and ultra wide band designs which cannot be catered by simple microstrip based designs. PIFAs have solved the problem to some extend, but the field of antennas needs more innovative designs In this thesis the design and development of compact planner antenna are presented. Emphasis is given to the design of the feed as well as the radiator resulting in simple compact uniplanar geometries. The Asymmetric coplanar feed used to excite the antennas is found to be a suitable choice for feeding compact antennas.The main objectives of the study are the design of compact single, dual and multi band antennas with uniplanar structure and extension of the design for practical GSM/WLAN applications and Ultra compact antennas using the above techniques and extension of the design to antennas for practical applications like RFID/DVB-H. All the above objectives are thoroughly studied. Antennas with ultra compact dimensions are obtained as a result of the study. Simple equations are provided to design antennas with the required characteristics. The design equations are verified by designing different antennas for different applications.

Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Compact asymmetric coplanar strip-fed antenna for wideband applications

An asymmetric coplanar strip-fed uniplanar antenna for wideband applications is presented. The resulting antenna offers a 2:1 VSWR bandwidth greater than 100% from 1.58 to 5.48 GHz covering the DCS/PCS/IEEE 802.11a/WiMAX bands. The antenna has an overall dimension of 44 × 35 mm2 when printed on a substrate of dielectric constant 4.4 and height 1.6 mm. The design equation is also presented in this article. The antenna exhibits good radiation characteristics and moderate gain in the entire operating band.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.