Amplitude Death: The emergence of stationarity in coupled nonlinear systems

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012

Oscillator phase noise: a tutorial

Linear time-invariant (LTI) phase noise theories provide important qualitative design insights but are limited in their quantitative predictive power. Part of the difficulty is that device noise undergoes multiple frequency translations to become oscillator phase noise. A quantitative understanding of this process requires abandoning the principle of time invariance assumed in most older theories of phase noise. Fortunately, the noise-to-phase transfer function of oscillators is still linear, despite the existence of the nonlinearities necessary for amplitude stabilization. In addition to providing a quantitative reconciliation between theory and measurement, the time-varying phase noise model presented in this tutorial identifies the importance of symmetry in suppressing the upconversion of 1/f noise into close-in phase noise, and provides an explicit appreciation of cyclostationary effects and AM-PM conversion. These insights allow a reinterpretation of why the Colpitts oscillator exhibits good performance, and suggest new oscillator topologies. Tuned LC and ring oscillator circuit examples are presented to reinforce the theoretical considerations developed. Simulation issues and the accommodation of amplitude noise are considered in appendixes

Nonlinear Design Technique for High-Power Switching-Mode Oscillators

A simple nonlinear technique for the design of high-efficiency and high-power switching-mode oscillators is presented. It combines existing quasi-nonlinear methods and the use of an auxiliary generator (AG) in harmonic balance. The AG enables the oscillator optimization to achieve high output power and dc-to-RF conversion efficiency without affecting the oscillation frequency. It also imposes a sufficient drive on the transistor to enable the switching-mode operation with high efficiency. Using this AG, constant-power and constant-efficiency contour plots are traced in order to determine the optimum element values. The oscillation startup condition and the steady-state stability are analyzed with the pole-zero identification technique. The influence of the gate bias on the output power, efficiency, and stability is also investigated. A class-E oscillator is demonstrated using the proposed technique. The oscillator exhibits 75 W with 67% efficiency at 410 MHz

Relaxation paths for single modes of vibrations in isolated molecules

A numerical simulation of vibrational excitation of molecules was devised, and used to excite computational models of common molecules into a prescribed, pure, normal vibration mode in the ground electronic state, with varying, controlable energy content. The redistribution of this energy (either non-chaotic or irreversible IVR) within the isolated, free molecule is then followed in time with a view to determining the coupling strength between modes. This work was triggered by the need to predict the general characters of the infrared spectra to be expected from molecules in interstellar space, after being excited by photon absorption or reaction with a radical. It is found that IVR from a pure normal mode is very "restricted" indeed at energy contents of one mode quantum or so. However, as this is increased, or when the excitation is localized, our approach allows us to isolate, describe and quantify a number of interesting phenomena, known to chemists and in non-linear mechanics, but difficult to demonstrate experimentally: frequency dragging, mode locking or quenching or, still, instability near a potential surface crossing, the first step to generalized chaos as the energy content per mode is increased.Comment: 25 pages, 15 figures; accepted by J. Atom. Phys.