Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.

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The Kuramoto model: A simple paradigm for synchronization phenomena

Substrate-integrated waveguide (SIW) technology represents an emerging and very promising candidate for the development of circuits and components operating in the microwave and millimetre-wave region. SIW structures are generally fabricated by using two rows of conducting cylinders or slots embedded in a dielectric substrate that connects two parallel metal plates, and permit the implementation of classical rectangular waveguide components in planar form, along with printed circuitry, active devices and antennas. This study aims to provide an overview of the recent advances in the modelling, design and technological implementation of SIW structures and components.

Review of substrate-integrated waveguide circuits and antennas

This paper describes three phase-shifterless beam steering techniques which exploit the synchronization properties of coupled nonlinear oscillator arrays. In each, the control parameters are the coupling phases of the local interactions between elements. The one-dimensional oscillator arrays under consideration are described by Phase Model-type equations, implying the assumption that the amplitude dynamics have achieved a steady state. Linear stability analyzes for each technique are provided which reveal significant differences in attainable scan angles.

Beam steering of nonlinear oscillator arrays through manipulation of coupling phases

An in-depth analysis of the nonlinear dynamics of coupled-oscillator arrays is presented for a better understanding of their complex autonomous behavior. In one-dimensional arrays, the constant inter-stage phase shift is varied by simultaneously detuning the two outermost oscillators in opposite directions. Thus, the array can be considered as a two-parameter system. Here, a two-parameter stability analysis of the oscillator array is carried out, investigating the phenomena that limit the achievable values of constant inter-stage phase shift under both weak and strong coupling conditions. The gradual evolution of the system behavior with increasing coupling strength is studied. A semianalytical approach is presented for an efficient design of the oscillator array, avoiding the computational expensiveness of harmonic balance (HB) in systems with a high number of oscillator elements. The proposed method, valid for weak coupling, uses a perturbation model of the elementary oscillator obtained with HB so it is of general application to any oscillator topology with accurate descriptions of its linear and nonlinear components. Approaches for the stability and phase-noise analyses based on this formulation are also presented. The new techniques have been applied to the design of a coupled system of three oscillators at 6 GHz. The results have been successfully compared with full HB simulations and with measurements

New Techniques for the Analysis and Design of Coupled-Oscillator Systems

The ability of coupled, nonlinear oscillator arrays to produce simultaneous beam steering and null generation is presented. This technique, which extends the capabilities of such arrays to include interference suppression, is realized through a generalization of Steyskal's method of pattern nulling by phase perturbation. An illustrative example is provided.

Simultaneous beam steering and null formation with coupled, nonlinear oscillator arrays

Nonlinear antennas combine advances in nonlinear dynamics, active antenna design, and analog microelectronics to generate beam steering and beam forming across an array of nonlinear oscillators. Nonlinear antennas exploit two phenomena typically shunned in traditional designs: nonlinear unit cells and interelement coupling. The design stems from nonlinear coupled differential equation analysis that by virtue of the dynamic control is far less complex than the linear counterparts by eliminating the need for phase shifters and beam forming computers. These advantages arise from incorporating nonlinear dynamics rather than limiting the system to linear quasisteady state operation. A theoretical framework describing beam shaping and beam forming by exploiting the phase, amplitude, and coupling dynamics of nonlinear oscillator arrays is presented. Experimental demonstration of nonlinear beam steering is realized using analog microelectronics.

D.W. Fogliatti

Papers

Nonlinear antenna technology