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Oscillatory nonlinear networks represent a circuit architecture for image and information processing. In particular they have associative properties and can be exploited for dynamic pattern recognition. In this manuscript the global dynamic behavior of weakly connected cellular networks of oscillators is investigated. It is assumed that each cell admits of a Lur'e description. In case of weak coupling the main dynamic features of the network are revealed by the phase deviation equation (i.e., the equation that describes the phase deviation due to the weak coupling). Firstly a very accurate analytic expression of the phase deviation equation is derived via the joint application of the describing function technique and of Malkin's Theorem. Then a complete analysis of the phase-deviation equation is carried out for 1-D arrays of oscillators. It is shown that the total number of periodic limit cycles with their stability properties can be estimated. Finally, in order to show the accuracy of the proposed approach, two networks containing second-order and third-order oscillators, respectively, are studied in detail. Index Terms--Bio-inspired networks, cellular nonlinear networks (CNNs), nonlinear dynamic networks, nonlinear oscillators, oscillatory networks.

Spectral techniques, like harmonic balance, are classical numerical tools for designing nonlinear oscillators and microwave circuits. Recently these techniques have been exploited for investigating complex dynamics in nonlinear systems. In this manuscript we firstly show that limit cycle Floquet's multipliers and the related bifurcation phenomena can be estimated through a spectral approach, entirely based on the describing function technique. Then we consider some significant case studies, and we show that our method yields more accurate results than the other describing function-based approaches proposed in the literature. Index Terms--Bifurcation, describing function, limit cycles, nonlinear systems.

The global dynamic behavior of a hysteretic oscillator is investigated. It is shown that the most significant bifurcation phenomena can be accurately detected through the joint application of two frequency-domain techniques, i.e., describing function and harmonic balance, and of a suitable time-domain method for computing limit-cycle Floquet's multipliers. The proposed approach can be effectively applied for investigating nonlinear oscillators and circuits that do not adroit of a simple Lur'e representation and that exhibit a complex dynamic behavior. Index Terms--Bifurcation, describing functions, harmonic balance (HB), hysteresis, nonlinear circuits.

A spectral technique is proposed for investigating periodic oscillations and bifurcations in cellular nonlinear networks. The method consists of the following three fundamental steps: 1) an accurate estimation of the whole set of stable and unstable limit cycles is provided through the application of the describing function technique; 2) a detailed characterization of each limit cycle is obtained via the harmonic balance (HB) technique, by exploiting as input parameter the single harmonic approximation, provided by the describing function technique; 3) limit cycle stability and bifurcations are studied by computing the Floquet's multipliers and exploiting both a time-domain and an HB-based technique. Index Terms--Cellular nonlinear networks (CNNs), complex dynamics, nonlinear dynamic arrays, oscillations, spectral techniques.

Cellular neural networks (CNNs) are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium-point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNNs, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements. Index Terms--Cellular neural networks (CNNs), equilibrium analysis, nonlinear circuits, stable equilibrium points.

Several variants of the Chua's circuit have been recently proposed in order to enlarge the class of nonlinear phenomena that can be generated by relatively simple circuits. In particular, Sharkovsky et al. proposed the so called time-delayed Chua's circuit (TDCC), where the original lumped LC resonator is substituted by an ideal transmission line, thereby generating an infinite dimensional system. The TDCC has been studied in details in the absence of the capacitor C, the only lumped dynamic element left in the circuit. This paper studies the effects of the presence of C on the dynamics of the circuit. After recasting the circuit equations in a suitable normalized form, their characteristic equation is theoretically investigated and the regions in the parameter space where all the eigenvalues have negative real part are exactly evaluated along with all the possible qualitative eigenvalue distributions. This analysis allows for a qualitative description of the TDCC dynamics in presence of the capacitor C. In particular, it is shown that, for particular sets of circuit parameters, an even small value of C, e.g., a parasitic element, may completely change the behavior of TDCC and that, on the other hand, any TDCC, exhibiting the period-adding phenomenon for C = 0, still continues to present this phenomenon even if a small capacitor C is added to the circuit. Index Terms - Bifurcation, chaos, nonlinear circuits.

The electromagnetic modeling of wave propagation along a semi-infinite wire with ground return is addressed. External excitation, via plane wave is considered. Both wire and ground plane are assumed to be perfect conductors. Through a spectral approach, a one-port Thevenin model of the structure, valid for any distance between wire and ground, is developed. Such a model allows to evaluate rigorously the limits and the accuracy of the transmission line (TL) equations.

The structure composed by a wire running above a ground plane and passing through an aperture in a semi-infinite metallic screen is analyzed from an electromagnetic point of view. We assume that the distance between the wire and the ground plane is sufficiently greater with respect to the aperture dimensions and that the latter are small in comparison with the free-space wavelength. A very accurate low frequency solution is obtained by representing the field quantities in a suitable spectral domain and by treating the wire current as a filament current. A transmission line model of the structure, based on the scattering parameter representation for both internal and external excitation, is derived. Then, by use of such a model, analytical expressions for an insertion loss and a signal-to-noise ratio (SNR) are obtained in order to assess the electromagnetic compatibility of the structure.

The canonical problem of an electromagnetic field incident on a metallic halfplane joined to a wire-mesh halfplane is considered. It is assumed that the wire radius is small in comparison with the spacing between the wires, and that this spacing is small with respect to the free-space wavelength. Under this hypothesis, it is shown that the problem can be solved in closed form by using a Wiener-Hopf technique for any nonuniform electromagnetic incident field. The field transmitted through the structure is computed, considering as uniform sources both TE and TM incident planewaves.

We investigate the steady-state electromagnetic field scattered by a nonlinear, frequency-dispersive magnetic or dielectric structure excited by a periodic field. For a planar structure under normal incidence, a 1D model holds, which can be simply interpreted in terms of a nonlinear, dispersive scalar or vector transmission line. The problem is solved by spatially discretizing the electric and magnetic fields; then, the lumped system is analyzed by means of fast algorithms for the steady-state analysis of nonlinear systems under periodic excitation. A comparative performance analysis of such algorithms (time-domain: shooting and extrapolation methods; frequency-domain: harmonic balance method) is carried out on case studies for both the dispersionless and dispersive cases The results obtained show that time-domain techniques compare favourably to frequency-domain methods.

In this paper the problem of the stability of Cellular Neural Networks (CNN's) and Delayed Cellular Neural Networks (DCNN's) is addressed by means of Lyapunov functions (functionals in the delayed case); new classes of nonpositive templates, describing CNN's and DCNN's, are shown to be stable and some conditions are found ensuring the complete stability of dominant template DCNN's and CNN's with nonmonotonic output functions.

A strange attractor has been found in a system described by a differential-difference equation: a delayed cellular neural network composed by only two cells; a detailed analysis of the set of eigenvalues that give rise to the attractor is presented and the bifurcation phenomena obtained by varying the delay are shown.

It is known that symmetric cellular neural networks (CNN's) are completely stable. In this paper it is shown that CNN's with delay (DCNN's), though symmetric, can become unstable if the delay if suitably chosen: actually such networks can exhibit periodic cycles. Moreover, a sufficient condition is presented to ensure complete stability: such a condition establishes a relation between the delay time and the parameters of the network.

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modeling the transition in high-Tc superconductors. The emergence of higher harmonics, besides the simple sinusoid Ic sin [lowercase_phi_synonym], is expected for dominant d-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act, respectively, by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO2 planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to p=1/8, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions. [ABSTRACT FROM AUTHOR]