Homoclinic Orbits In Slowly Varying Oscillators

We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time. We show how the results on periodic orbits of the preceding paper are related to the present homoclinic results, and apply them to a periodically forced Duffing equation with weak feedback

A horseshoe in the dynamics of a forced beam

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Reviews

A. Barker and F. Manji, Writing for Change ‐ An Interactive Guide to Effective Writing, Writing for Science, Writing for Advocacy, CD‐ROM and Users Guide, Fahama/International Development Research Centre, Oxford, 2000. ISBN: 0–9536–9021–0, no price given. Softback (28 pages) and CD‐ROM

Explicit moments of decision times for single- and double-threshold drift-diffusion processes

We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for accuracy, mean DT and coefficient of variation are readily available, third and higher moments and conditioned moments are not generally available. We provide explicit formulae for these, describe their behaviors as drift rates and starting points approach interesting limits, and, with the support of numerical simulations, discuss how trial-to-trial variability of drift rates, starting points, and non-decision times affect these behaviors in the extended diffusion model. Both unconditioned moments and those conditioned on correct and erroneous responses are treated. We argue that the results will assist in exploring mechanisms of evidence accumulation and in fitting parameters to experimental data

Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups

Abstract not availabl

Nonlinear Propagation of Light in One Dimensional Periodic Structures

We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion), the periodic structure (photonic band dispersion) and nonlinearity. We present a detailed discussion of the role of these effects individually and in concert. We derive the nonlinear coupled mode equations (NLCME) which govern the envelope of the coupled backward and forward components of the electromagnetic field. We prove the validity of the NLCME description and give explicit estimates for the deviation of the approximation given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known to have gap soliton states. A consequence of our results is the existence of very long-lived {\it gap soliton} states of AMLE. We present numerical simulations which validate as well as illustrate the limits of the theory. Finally, we verify that the assumptions of our model apply to the parameter regimes explored in recent physical experiments in which gap solitons were observed.Comment: To appear in The Journal of Nonlinear Science; 55 pages, 13 figure

The economics of stock index futures: Theory and evidence

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis aims to provide detailed investigation into the role and functioning of the FTSE-100 stock index futures contract, by examining four interrelated issues. Chapter 1 reviews the literature, demonstrating that stock index futures can increase investor utility by offering hedging and investment opportunities. Further, the price discovery role of futures is discussed. Chapter 2 investigates the risk return relationship for the FTSE-100 contract within a CAPM framework. While CAPM adequately explains returns prior to October 1987, post-crash the contract is riskier and excess returns and a day of the week effect are evident. Chapter 3 examines the impact of futures on the underlying spot market using GARCH, which allows examination of the link between information and volatility. While spot prices are more volatile post-futures, this is due to more rapid impounding of information. The view that futures destabilise spot markets and should be subject to further regulation is questioned. Chapter 4 examines futures market efficiency using the Johansen cointegration procedure and variance bounds tests which are developed here. Results suggest futures prices provide unbiased predictions of future spot prices for 1, 2 and 4 months prior to maturity of the contract. For 3, 5 and 6 months prior to maturity the unbiasedness hypothesis does not hold. Chapter 5 discusses the major role of futures; hedging. Hedge ratios and hedging effectiveness are examined in relation to duration and expiration effects. Hedge ratio stability is also examined. Finally, hedging strategies based on historical information are examined. Results show there are duration and expiration effect, hedge ratios are stationary and using historical information does not greatly reduce hedging effectiveness. The FTSE-100 contract is shown to be a highly effective means by which to hedge risk. Chapter 6 provides a summary and concluding remarks concerning the relevance of the research carried out here