1,419 research outputs found
BAL: A library for the brute-force analysis of dynamical systems
No full textThis paper describes the functionality and usage of bal, a C/C++ library with a Python front-end for the brute-force analysis of continuous-time dynamical systems described by ordinary differential equations (ODEs). bal provides an easy-to-use wrapper for the efficient numerical integration of ODEs and, by detecting intersections of the trajectory with appropriate Poincaré sections, allows to classify the asymptotic trajectory of a dynamical system for bifurcation analysis. Some examples of application are discussed, concerning two-dimensional bifurcation diagrams, Lyapunov exponents and finite-time Lyapunov exponents, basins of attraction, simulation of switching ODE systems, and integration with AUTO, a software package for continuation analysis.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Nonlinear behavioural model of charge pump PLLs
No full textDespite the nonlinear nature of even the simplest versions of phase locked loops (PLLs), linear models are still used during the first phases of the design of modern PLLs. Even though the linear model may represent a crude approach, its use is justified by the fact that accurate numerical simulations often require a too large amount of CPU time, being PLLs by construction stiff circuits, characterised by very different time scales.
This aspect has triggered the need for compact models that allow fast and accurate numerical simulations. The scientific literature numbers several models that have been developed with different approaches and tailored to different simulation environments. In this context, we propose a nonlinear model of a type-II PLL, which (1) considers both the switching behaviour of the phase/frequency detector and charge pump and the complex dynamics (including the presence of amplitude and phase noise) of the voltage controlled oscillator, (2) is compact and can be easily implemented in modern mixed analog/digital simulators as a behavioural block, and (3) allows the simulation of spurs owing to the nonlinearities of both the charge pump and the fractional frequency divider
Computational Modelling of the Brain: Modelling Approaches to Cells, Circuits and Networks
No full textThis volume offers an up-to-date overview of essential concepts and modern approaches to computational modelling, including the use of experimental techniques related to or directly inspired by them. The book introduces, at increasing levels of complexity and with the non-specialist in mind, state-of-the-art topics ranging from single-cell and molecular descriptions to circuits and networks.
Four major themes are covered, including subcellular modelling of ion channels and signalling pathways at the molecular level, single-cell modelling at different levels of spatial complexity, network modelling from local microcircuits to large-scale simulations of entire brain areas and practical examples. Each chapter presents a systematic overview of a specific topic and provides the reader with the fundamental tools needed to understand the computational modelling of neural dynamics.
This book is aimed at experimenters and graduate students with little or no prior knowledge of modelling who are interested in learning about computational models from the single molecule to the inter-areal communication of brain structures. The book will appeal to computational neuroscientists, engineers, physicists and mathematicians interested in contributing to the field of neuroscience
Isomorphic Circuit Clustering for Fast and Accurate Electromagnetic Transient Simulations of MMCs
No full textModular multilevel converters have become the technology of choice in high voltage direct current systems. They are composed of a large number of submodules, which poses significant computational challenges to electromagnetic transient simulations. To address this issue, scholars proposed several approaches that are a trade-off between simulation accuracy and computational burden, which mainly achieve numerical efficiency by adopting reduced and simplified models of the converter arm submodules. This paper proposes a different simulation paradigm based on sub-circuit isomorphism. It is suited for the analysis of intrinsically modular electronic circuits, as it exploits the common behavior of structurally identical submodules by clustering them together. This method does not require any simplification of the submodule electrical model and minimizes the number of equations to be solved at each time step of the time domain analysis, thereby significantly reducing the computational effort. Thus, this method is suitable for thorough simulations of ac/dc networks, which may require the implementation of detailed transistor-level representations of the converter submodules
Synchronization: a tool for validating a PWL circuit that approximates the Hindmarsh-Rose neuron model
No full textThis paper uses synchronization as a tool for further validating a circuit (HR-PWL circuit) recently proposed in the literature and based on a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model. The accuracy of the single neuron hardware implementation has been already validated through bifurcation analysis tools. Here, the synchronization behavior of networks formed by HR neurons is simulated and compared to that of companion networks of PWL neurons, with the purpose of validating the HR-PWL circuit also from a collective behavior point of view. In the considered cases, the neurons are connected either by linear diffusive or by nonlinear sigmoidal coupling, with different topologies. The analysis is based on the Master Stability Function approach and is verified by extensive numerical time-domain simulations. The synchronization properties of the PWL neuron networks turn out to be qualitatively very similar to those of the companion HR networks, confirming the validity of the proposed hardware-implemented neuron
Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation.
No full textStochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here
A method based on a genetic algorithm to find PWL approximations of multivariate nonlinear functions
No full textIn this paper we present a systematic approach to find piecewise-linear approximations of multivariate continuous nonlinear functions, by ensuring a good trade-off between approximation accuracy and model complexity. The proposed (suboptimal) method is based on genetic programming and takes into account the circuit constraints concerning the lower bounds for the size of each domain region (called simplex) where a given nonlinear function is approximated linearly. As a benchmark example, we approximate the well-known Hodgkin- Huxley neuron model
Modelling the Effects of Early Exposure to Alcohol on the Excitability of Cortical Neurons
No full textIn recent years, a novel approach based on multi-objective optimization has been developed to automatically tune biophysically realistic, multi-compartmental neuron models starting from electrophysiological recordings. Here, we apply this methodology to the optimization of model neurons capable of reproducing the reduced excitability observed in experiments carried out in cortical pyramidal cells in a rodent model of fetal alcohol spectrum disorder. We find that both control and ethanol-exposed model cells present an excellent match with the experiments in terms of membrane voltage dynamics, with the latter group displaying a small but significant rightward shift of their current-frequency relationship. We identify a possible interplay between model parameters and cellular morphology and suggest future improvements to better capture the features of dendritic voltage dynamics
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