Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS?

This work shows how using specifically selected or designed waveforms in wireless power transfer (WPT) systems can lead to improved RF to dc conversion efficiency in rectifier circuits in the receiving end of these systems Signals with different time domain waveforms are considered such as OFDM, white noise and chaotic waveforms, and the performance of a rectifier circuit operating at 433 MHz is evaluated when using these signals in comparison to a single carrier constant envelope signal The performed experiments show that selecting high peak to average power ratio (PAPR) signals lead to improved RF-DC conversion efficiency in rectifier circuits

Optimal Waveforms for Efficient Wireless Power Transmission

In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.

Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit.

This paper presents the system architecture, modeling, and design constraints for a baseband, integrated, CMOS, impulse ultra-wideband transceiver targeting very low power consumption on the order of 1 mW. Intended for a sensor network application, the radio supports low communication rates (/spl sim/100 kpbs) and ranging capabilities over short distances (/spl sim/10 m). Based on a "mostly digital" architecture, the analog complexity is reduced by moving the A/D convertor as close to the antenna as is reasonable. Pulses are generated from simple digital switches, overlaying the signal energy on the lower FCC UWB band (0-960 MHz). Reception is achieved using baseband gain blocks feeding a time-interleaved bank of low resolution A/D converters. A window of energy is captured in time and fed to the digital backend for processing. To save power and area, the digital backend implements only a pulse template correlation filter block overlaid with an additional spreading code. As a pulse template is used, no specific channel estimation or interference cancellation is assumed. The system performance is quantified for this case and implementation tradeoffs are explored with a strong focus on reducing power consumption. In particular, the issues of modulation choice, clock generation, gain and noise figure, ADC resolution, and digital signal processing requirements will be discussed.

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An ultra-wideband transceiver architecture for low power, low rate, wireless systems

In the present paper, a new memristor based oscillator is obtained from the autonomous Jerk circuit [Kengne et al., Nonlinear Dynamics (2016) 83: 751765] by substituting the nonlinear element of the original circuit with a first order memristive diode bridge. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. Various nonlinear analysis tools such as phase portraits, time series, bifurcation diagrams, Poincare section and the spectrum of Lyapunov exponents are exploited to characterize different scenarios to chaos in the novel circuit. It is found that the system experiences period doubling and crisis routes to chaos. One of the major results of this work is the finding of a window in the parameters’ space in which the circuit develops hysteretic behaviors characterized by the coexistence of four different (periodic and chaotic) attractors for the same values of the system parameters. Basins of attractions of various coexisting attractors are plotted showing complex basin boundaries. As far as the authors’ knowledge goes, the novel memristive jerk circuit represents one of the simplest electrical circuits (no analog multiplier chip is involved) capable of four disconnected coexisting attractors reported to date. Both PSpice simulations of the nonlinear dynamics of the oscillator and laboratory experimental measurements are carried out to validate the theoretical analysis.

Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit

This paper reports a methodological approach to the analysis and design of sinusoidal oscillators based on bifurcation analysis. The simple Colpitts oscillator is taken as an example to demonstrate this nonlinear approach for both the nearly sinusoidal and chaotic modes of operation. In particular, it is shown how regular and irregular (chaotic) oscillations can be generated, depending on the circuit parameters.

Nonlinear analysis of the Colpitts oscillator and applications to design

In this paper, we propose a pseudo-chaotic modulation suitable for ultrawide-bandwidth impulse-radio communication systems. The coding scheme is based upon controlling the symbolic dynamics of a chaotic map for encoding the digital information to be transmitted. The pseudo-chaotic time hopping enhances the spread-spectrum characteristics of the system, by removing most periodic components from the transmitted signal. A maximum-likelihood detector for the proposed scheme is presented and its scalability features are illustrated. Finally, theoretical performance bounds for both soft and hard Viterbi decoding are derived and compared with the simulation results.

Pseudo-chaotic time hopping for UWB impulse radio

This paper presents an experimental verification of the theoretical predictions, recently published in [Maggio et al., 1999; De Feo et al., 2000], about the bifurcation phenomena occurring in the Colpitts oscillator. Specifically, we performed an automated series of simulations based on the Spice model and, more importantly, a computer-assisted set of measurements on a concrete realization of the oscillator. It turns out that the bifurcation phenomena exhibited by the oscillator are relatively independent of the simplifying assumptions on the transistor model. Moreover, it is shown that the predicted behaviors can be reproduced experimentally, both qualitatively and quantitatively, in a robust way.

Bifurcations in the colpitts oscillator: from theory to practice

In this paper, a general methodology for predicting the amplitude of oscillation in nearly sinusoidal oscillators is presented. The method relies on the recently proposed projection technique for the computation of the center manifold and on the Hopf normal form theory to approximate the corresponding limit cycle in state space. The Colpitts oscillator is selected as a case study and, for this circuit, a closed-form expression for the amplitude of oscillation is derived as a function of the circuit parameters.

A general method to predict the amplitude of oscillation in nearly sinusoidal oscillators

A method is for decoding a pulse signal modulated through a transmitted reference modulation scheme The modulated pulse signal may include, repetitively, a reference pulse followed by an information pulse delayed with a delay The method may include subtracting or adding from the modulated pulse signal, a version of the modulated pulse signal delayed with the delay for obtaining a processed signal, and performing a non-coherent detection on the processed signal

G.M. Maggio

Papers

Nonlinear analysis of the Colpitts oscillator and applications to design

Pseudo-chaotic time hopping for UWB impulse radio

Bifurcations in the colpitts oscillator: from theory to practice

A general method to predict the amplitude of oscillation in nearly sinusoidal oscillators

Method of coding and decoding a pulse signal, in particular an uwb-ir signal, and corresponding devices