I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

The organization of behavior: A neuropsychological theory

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

Differential Equations and Dynamical Systems

A thorough investigation of the nonlinear dynamics of networks of memristor oscillators is a key step towards the design of systems based upon them, such as neuromorphic circuits and dense nonvolatile memories. A wide gamut of complex dynamic behaviors, including chaos, is observed even in a simple network of memristor oscillators, proposed here as a good candidate for the realization of oscillatory associative and dynamic memories. A detailed study of number and stability of all periodic and nonperiodic oscillations appearing in the network may not leave aside a preliminary deep understanding of the local and global behavior of the basic oscillator. Depending on two bifurcation parameters, controlling memristor nonlinearity, the oscillator exhibits different dynamic behaviors, analyzed here through application of state-of-the-art techniques from the theory of nonlinear dynamics to the oscillator model.

Nonlinear Dynamics of Memristor Oscillators

Since the 2008-dated discovery of memristor behavior at the nano-scale, Hewlett Packard is credited for, a large deal of efforts have been spent in the research community to derive a suitable model able to capture the nonlinear dynamics of the nano-scale structures. Despite a considerable number of models of different complexity have been proposed in the literature, there is an ongoing debate over which model should be universally adopted for the investigation of the unique opportunities memristors may offer in integrated circuit design. In order to shed some light into this passionate discussion, this paper compares some of the most noteworthy memristor models present in the literature. The strength of the Pickett?s model stands in its experiment-based development and in its ability to describe some physical mechanism at the origin of memristor dynamics. Since its parameter values depend on the excitation of the memristor and/or on the circuit employing the memristor, it may be assumed as a reference for comparison only in those scenarios for which its parameters were reported in the literature. In this work various noteworthy memristor models are fitted to the Pickett's model under one of such scenarios. This study shows how three models, Biolek's model, the Boundary Condition Memristor model and the Threshold Adaptive Memristor model, outperform the others in the replica of the dynamics observed in the Pickett's model. In the second part of this work the models are used in a couple of basic circuits to study the variance between the dynamical behaviors they give rise to. This analysis intends to make the circuit designers aware of the different behaviors which may occur in memristor-based circuits according to the memristor model under use.

Memristor Model Comparison

The class of nonlinear dynamical systems known as memristive systems was defined by Chua and Kang back in 1976. Since then, many studies have addressed the search for physically-realisable memristive systems. In this reported work, it is proved that the class of memristive systems encloses an elementary electronic circuit comprising a full-wave rectifier with a second-order RLC filter.

Memristive diode bridge with LCR filter

A deep theoretical discussion proves that in Joglekar's and Biolek's models the memductance-flux relation of a memristor driven by a sign-varying voltage source may only exhibit single-valuedness and multi-valuedness respectively. This manuscript derives a novel boundary condition-based Model for memristor nanostructures. Unlike previous models, the proposed one allows for closed-form solutions. More importantly, subject to the nonlinear behavior under exam, this model enables a suitable tuning of boundary conditions, which may result in the detection of both single-valued and multi-valued memductance-flux relations under certain sign-varying inputs of interest. The large class of modeled dynamics include all behaviors reported in the legendary paper revealing the existence of memory-resistance at the nano scale.

A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures

Memristor-based circuits are widely exploited to realize analog and/or digital systems for a broad scope of applications (e.g., amplifiers, filters, oscillators, logic gates, and memristor as synapses). A systematic methodology is necessary to understand complex nonlinear phenomena emerging in memristor circuits. The manuscript introduces a comprehensive analysis method of memristor circuits in the flux-charge $(\varphi,q)$ -domain. The proposed method relies on Kirchhoff Flux and Charge Laws and constitutive relations of circuit elements in terms of incremental flux and charge. The main advantages (over the approaches in the voltage-current $(v,i)$ -domain) of the formulation of circuit equations in the $(\varphi,q)$ -domain are: a) a simplified analysis of nonlinear dynamics and bifurcations by means of a smaller set of ODEs; b) a clear understanding of the influence of initial conditions. The straightforward application of the proposed method provides a full portrait of the nonlinear dynamics of the simplest memristor circuit made of one memristor connected to a capacitor. In addition, the concept of invariant manifolds permits to clarify how initial conditions give rise to bifurcations without parameters.

/pdf/memristor-circuits-flux-charge-analysis-method-2y9ql5whso.pdf

Fernando Corinto

Papers

Nonlinear Dynamics of Memristor Oscillators

Memristor Model Comparison

Memristive diode bridge with LCR filter

A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures

Memristor Circuits: Flux—Charge Analysis Method