Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the birth of the SNA which we term as the \emph{bubbling route to SNA}. We characterize and confirm this birth from both experimental and numerical data by maximal Lyapunov exponents and their variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution function. We also strongly confirm the birth of SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.

Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a negative conductance series LCR circuit with a diode both numerically and experimentally. The birth of SNAs by these three routes is verified from both experimental and their corresponding numerical data by maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier amplitude spectrum, spectral distribution function and finite-time Lyapunov exponents. Although these three routes have been identified numerically in different dynamical systems, the experimental observation of all these mechanisms is reported for the first time to our knowledge and that too in a single second order electronic circuit.Comment: 21 figure

Resonant Tunnelling Optoelectronic Circuits

Nowadays, most communication networks such as local area networks (LANs), metropolitan area networks (MANs), and wide area networks (WANs) have replaced or are about to replace coaxial cable or twisted copper wire with fiber optical cables. Light-wave communication systems comprise a transmitter based on a visible or near-infrared light source, whose carrier is modulated by the information signal to be transmitted, a transmission media such as an optical fiber, eventually utilizing in-line optical amplification, and a receiver based on a photo-detector that recovers the information signal (Liu, 1996)(Einarsson, 1996). The transmitter consists of a driver circuit along a semiconductor laser or a light emitting diode (LED). The receiver is a signal processing circuit coupled to a photo-detector such as a photodiode, an avalanche photodiode (APD), a phototransistor or a high speed photoconductor that processes the photo-detected signal and recovers the primitive information signa

Applications of dynamical systems with symmetry

This thesis examines the application of symmetric dynamical systems theory to two areas in applied mathematics: weakly coupled oscillators with symmetry, and bifurcations in flame front equations. After a general introduction in the first chapter, chapter 2 develops a theoretical framework for the study of identical oscillators with arbitrary symmetry group under an assumption of weak coupling. It focusses on networks with 'all to all' Sn coupling. The structure imposed by the symmetry on the phase space for weakly coupled oscillators with Sn, Zn or Dn symmetries is discussed, and the interaction of internal symmetries and network symmetries is shown to cause decoupling under certain conditions. Chapter 3 discusses what this implies for generic dynamical behaviour of coupled oscillator systems, and concentrates on application to small numbers of oscillators (three or four). We find strong restrictions on bifurcations, and structurally stable heteroclinic cycles. Following this, chapter 4 reports on experimental results from electronic oscillator systems and relates it to results in chapter 3. In a forced oscillator system, breakdown of regular motion is observed to occur through break up of tori followed by a symmetric bifurcation of chaotic attractors to fully symmetric chaos. Chapter 5 discusses reduction of a system of identical coupled oscillators to phase equations in a weakly coupled limit, considering them as weakly dissipative Hamiltonian oscillators with very weakly coupling. This provides a derivation of example phase equations discussed in chapter 2. Applications are shown for two van der Pol-Duffing oscillators in the case of a twin-well potential. Finally, we turn our attention to the Kuramoto-Sivashinsky equation. Chapter 6 starts by discussing flame front equations in general, and non-linear models in particular. The Kuramoto-Sivashinsky equation on a rectangular domain with simple boundary conditions is found to be an example of a large class of systems whose linear behaviour gives rise to arbitrarily high order mode interactions. Chapter 7 presents computation of some of these mode interactions using competerised Liapunov-Schmidt reduction onto the kernel of the linearisation, and investigates the bifurcation diagrams in two parameters

Integrated RF oscillators and LO signal generation circuits

This thesis deals with fully integrated LC oscillators and local oscillator (LO) signal generation circuits. In communication systems a good-quality LO signal for up- and down-conversion in transmitters is needed. The LO signal needs to span the required frequency range and have good frequency stability and low phase noise. Furthermore, most modern systems require accurate quadrature (IQ) LO signals. This thesis tackles these challenges by presenting a detailed study of LC oscillators, monolithic elements for good-quality LC resonators, and circuits for IQ-signal generation and for frequency conversion, as well as many experimental circuits. Monolithic coils and variable capacitors are essential, and this thesis deals with good structures of these devices and their proper modeling. As experimental test devices, over forty monolithic inductors and thirty varactors have been implemented, measured and modeled. Actively synthesized reactive elements were studied as replacements for these passive devices. At first glance these circuits show promising characteristics, but closer noise and nonlinearity analysis reveals that these circuits suffer from high noise levels and a small dynamic range. Nine circuit implementations with various actively synthesized variable capacitors were done. Quadrature signal generation can be performed with three different methods, and these are analyzed in the thesis. Frequency conversion circuits are used for alleviating coupling problems or to expand the number of frequency bands covered. The thesis includes an analysis of single-sideband mixing, frequency dividers, and frequency multipliers, which are used to perform the four basic arithmetical operations for the frequency tone. Two design cases are presented. The first one is a single-sideband mixing method for the generation of WiMedia UWB LO-signals, and the second one is a frequency conversion unit for a digital period synthesizer. The last part of the thesis presents five research projects. In the first one a temperature-compensated GaAs MESFET VCO was developed. The second one deals with circuit and device development for an experimental-level BiCMOS process. A cable-modem RF tuner IC using a SiGe process was developed in the third project, and a CMOS flip-chip VCO module in the fourth one. Finally, two frequency synthesizers for UWB radios are presented

Experimental and theoretical investigations into the switching of liquid crystal devices

This work addresses the dynamic switching of liquid crystal cells. While static measurements of the permittivity liquid crystal cells are well established, here a novel transient permittivity technique is developed and applied to several liquid crystalline substances in a variety of geometries. This technique utilises A.C. waveforms to measure the permittivity of a cell during the dynamic processes of switching and relaxing, allowing a detailed picture of the switching process to be constructed on small time scales. The results for several materials are presented and compared to theoretical predictions stemming from standard liquid crystal continuum theory. The technique is expanded to utilise frequency modulation when applied to dual frequency materials and is adapted to D.C. fields. Novel experimental results concerning surface stabilised ferroelectric liquid crystals have recently shown an unexpected second minimum in the tau-V response curve. The origin of this phenomenon is explored via a numerical simulation program and a qualitative explanation found regarding the torque generated by the surface alignment that is consistent with established theory

The Cavity-Embedded Cooper Pair Transistor as a Charge Detector Operating in the Nonlinear Regime

The cavity-embedded Cooper pair transistor (cCPT) has been shown to be a nearly quantum limited charge detector operating with only a single intracavity photon. Here, we use the inherent Kerr nonlinearity to demonstrate a dispersive charge sensing technique inspired by the Josephson bifurcation amplifier. Operating in the bistable regime close to a bifurcation edge, the cCPT is sensitive to charge shifts of 0.09e in a single-shot readout scheme with a detection time of 3 μs and a detection fidelity of 94%. The readout is implemented with only ∼ 25 intracavity photons in the high oscillation amplitude state, still several orders of magnitude lower than drives used in state-of-the-art radio frequency single electron transistors (rf-SETs). We find that a major limitation to the charge sensitivity of the device is fluctuation-induced switching between the metastable oscillation states in the bistable region. We study the lifetimes of these states across the gate and flux range of the cCPT and find that the switching properties depend on the strength of the Kerr nonlinearity at the cCPT bias point. We also explore a second nonlinear detection scheme where we parametrically pump the cCPT using a time-varying flux close to twice its resonance frequency to induce parametric oscillations. Flux pumping at a detuning on the edge of the parametric oscillation threshold makes the amplitude of oscillations sensitive to the charge environment. With no input drive, we are able to distinguish charge states ∼ 0.1e apart in a measurement time of 1 μs with a fidelity of 83%. The cCPT is a rich nonlinear system in which we observe sub-harmonic oscillations and phase coherent degenerate parametric amplification which could potentially be used to enhance the dispersive charge sensing of the device operating with a single intracavity photon level drive