Periodic visual stimulation and analysis of the resulting steady-state visual evoked potentials were first introduced over 80 years ago as a means to study visual sensation and perception. From the first single-channel recording of responses to modulated light to the present use of sophisticated digital displays composed of complex visual stimuli and high-density recording arrays, steady-state methods have been applied in a broad range of scientific and applied settings.The purpose of this article is to describe the fundamental stimulation paradigms for steady-state visual evoked potentials and to illustrate these principles through research findings across a range of applications in vision science.

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The steady-state visual evoked potential in vision research: A review.

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation phenomena and attractors. The circuit consists of two capacitors, an inductor, a linear resistor, and a nonlinear resistor. This paper describes the design methodology for a robust practical op amp implementation of Chua's circuit. In addition, we present experimental results and SPICE simulations for a working circuit using o -the-shelf components.

http://nonlinear.eecs.berkeley.edu/chaos/RobustOpAmpRealizationOfChuaCircuit.pdf

Robust OP Amp realization of Chua's circuit

https://www.dtc.umn.edu/s/resources/gg-se.pdf

A bibliography on nonlinear system identification

In this study, digital higher-order spectral analysis and frequency-domain Volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time-invariant systems up to third order. The primary focus is on consideration of random excitation of nonlinear systems and, thus, the approach makes extensive use of higher-order spectral analysis to determine the frequency-domain Volterra kernels, which correspond to linear, quadratic, and cubic transfer functions. Although the Volterra model is nonlinear in terms of its input, it is linear in terms of its unknown transfer functions. Thus, a least squares approach is used to determine the optimal (in a least squares sense) set of linear, quadratic, and cubic transfer functions. Of particular practical note, is the fact that the approach of this paper is valid for non-Gaussian, as well as Gaussian, random excitation. It may also be utilized for multitone inputs. The complexity of the problem addressed in this paper arises from two principal causes: (1) the necessity to work in a 3D frequency space to describe cubically nonlinear systems, and (2) the necessity to characterize the non-Gaussian random excitation by computing higher-order spectral moments up to sixth order. A detailed description of the approach used to determine the nonlinear transfer functions, including considerations necessary for digital implementation, is presented. >

Application of higher order spectral analysis to cubically nonlinear system identification

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

Accurate measurement of Volterra kernels is an essential step in the modelling of weakly non-linear physical systems via the block box approach, and in model validation. This paper is a sequel to an earlier paper,1 where practical methods for measuring Volterra kernels were presented along with a quick method for measuring the second-order Volterra kernels. This paper extends that quick method for measuring higher-order frequency-domain Volterra kernels of weakly non-linear systems. We further developed the quick method to measure directly the points of the Volterra kernels which are located along one or more axes in the frequency domain, thus making our method complete and more accurate than that presented in Reference 1. We illustrate our method by actually measuring a weakly non-linear circuit whose Volterra kernels can be accurately calculated. the experimentally measured and the theoretically predicted results agree remarkably well.

Measuring Volterra kernels (II)

Efficient methods were previously given for measuring the frequency-domain transfer functions, namely Volterra kernels of weakly non-linear systems. the success of these methods depends crucially on the assumption that the highest significant order of the system under test is known. Practical algorithms for determining the highest significant order of non-linear systems are presented in this paper. Our algorithm can be used not only to validate the measurement results obtained by the methods presented earlier but is also capable of determining whether a Volterra series representation actually exists for the system under test.

Measuring volterra kernels III: How to estimate the highest significant order

Self-similar bifurcation structures from chua's circuit

This paper presents several new algorithms which are used to implement two recently published uniqueness theorems applicable to nonlinear resistive circuits containing independent sources, two-terminal resistors and linear controlled sources. These programs are novel in that they allow a computer to test directly for qualitative behavior. The algorithms and the two programs which use them are described and results are presented for some examples from the original papers.

Youlin Liao

Papers

Measuring Volterra kernels (II)

Measuring volterra kernels III: How to estimate the highest significant order

Self-similar bifurcation structures from chua's circuit

Qualitative nonlinear circuit analysis using computers