iv List of figures v List of tables v

The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.

I review the local theory of mixing, which focuses on infinitesimal blobs of scalar being advected and stretched by a random velocity field. An advantage of this theory is that it provides elegant analytical results. A disadvantage is that it is highly idealised. Nevertheless, it provides insight into the mechanism of chaotic mixing and the effect of random fluctuations on the rate of decay of ...

The extent of chaos and the suppressory role of Coulomb repulsion in the chaotic dynamics associated with nonsteady finite-amplitude electroconvection is revisited in the context of dynamical systems. Specifically, it is theoretically demonstrated that the threshold value of the charge density taming the heteroclinic chaos associated with laminar chaotic mixing depends on the sinusoidal perturb...

We present a study of the recently discovered spatially-extended chaotic state known as spiral-defect chaos, which occurs in low-Prandtl-number, largeaspect-ratio Rayleigh-Bénard convection. We employ the modulus squared of the space-time Fourier transform of time series of two-dimensional shadowgraph images to construct the structure factor S(~k, ω). This analysis is used to characterize the a...

We consider the statistics of the impedance Z of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental Z data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized impedance whose probability density function is predicted to be universal in that it depends only on the loss (qua...

How to construct a measurement matrix with good performance and easy hardware implementation is the core research problem in compressed sensing. In this paper, we present a simple and efficient measurement matrix named Incoherence Rotated Chaotic (IRC) matrix. We take advantage of the well pseudorandom of chaotic sequence, introduce the concept of the incoherence factor and rotation, and adopt ...

Software for the resolution of certain kind of problems, those that rate high in the Stringent Performance Objectives adjustment factor (IFPUG scheme), can be described using a combination of game theory and autonomous systems. From this description it can be shown that some of those problems exhibit chaotic behavior, an important fact in understanding the functioning of the related software. A...

This paper presents a modified Differential Evolution (DE) algorithm called OCMODE for solving multi-objective optimization problems. First, the initialization phase is improved by using the opposition based learning. Further, a time varying scale factor F employing chaotic sequence is used which helps to get a well distributed Pareto front by the help of non dominated and crowding distance sor...

A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory number statistics for the model of a nonlinear dissipative oscillator. It is shown that the probability distributions and variances of oscillatory number states are strongly transformed in the order-to-chaos transition. A nonclassical, sub-Poissonian statistics of oscillatory excitation numbers is est...