Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

A dynamic causal model of the coupling between pulse stimulation and neural activity

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers. The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1–40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different. Following Friston, Mechelli, Turner, and Price (2000), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

Time-lag in biological responses to landscape changes in a highly dynamic Atlantic forest region

Time-lagged responses of biological variables to landscape modifications are widely recognized, but rarely considered in ecological studies. In order to test for the existence of time-lags in the response of trees, small mammals, birds and frogs to changes in fragment area and connectivity, we studied a fragmented and highly dynamic landscape in the Atlantic forest region. We also investigated the biological correlates associated with differential responses among taxonomic groups. Species richness and abundance for four taxonomic groups were measured in 21 secondary forest fragments during the same period (2000-2002), following a standardized protocol. Data analyses were based on power regressions and model selection procedures. The model inputs included present (2000) and past (1962, 1981) fragment areas and connectivity, as well as observed changes in these parameters. Although past landscape structure was particularly relevant for trees, all taxonomic groups (except small mammals) were affected by landscape dynamics, exhibiting a time-lagged response. Furthermore, fragment area was more important for species groups with lower dispersal capacity, while species with higher dispersal ability had stronger responses to connectivity measures. Although these secondary forest fragments still maintain a large fraction of their original biodiversity, the delay in biological response combined with high rates of deforestation and fast forest regeneration imply in a reduction in the average age of the forest. This also indicates that future species losses are likely, especially those that are more strictly-forest dwellers. Conservation actions should be implemented to reduce species extinction, to maintain old-growth forests and to favour the regeneration process. Our results demonstrate that landscape history can strongly affect the present distribution pattern of species in fragmented landscapes, and should be considered in conservation planning. (C) 2009 Elsevier Ltd. All rights reserved.

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.

Domain wall contribution to dielectric and piezoelectric responses in 0.65Pb(Mg1/3Nb2/3)-0.35PbTiO(3) ferroelectric ceramics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.

Involvement of N-methyl-d-aspartate glutamate receptor and nitric oxide in cardiovascular responses to dynamic exercise in rats

Dynamic exercise evokes sustained cardiovascular responses, which are characterized by arterial pressure and heart rate increases. Although it is well accepted that there is central nervous system mediation of cardiovascular adjustments during exercise, information on the role of neural pathways and signaling mechanisms is limited. It has been reported that glutamate, by acting on NMDA receptors, evokes the release of nitric oxide through activation of neuronal nitric oxide synthase (nNOS) in the brain. In the present study, we tested the hypothesis that NMDA receptors and nNOS are involved in cardiovascular responses evoked by an acute bout of exercise on a rodent treadmill. Moreover, we investigated possible central sites mediating control of responses to exercise through the NMDA receptor-nitric oxide pathway. Intraperitoneal administration of the selective NMDA glutamate receptor antagonist dizocilpine maleate (MK-801) reduced both the arterial pressure and heart rate increase evoked by dynamic exercise. Intraperitoneal treatment with the preferential nNOS inhibitor 7-nitroindazole reduced exercise-evoked tachycardiac response without affecting the pressor response. Moreover, treadmill running increased NO formation in the medial prefrontal cortex (MPFC), bed nucleus of the stria teminalis (BNST) and periaqueductal gray (PAG), and this effect was inhibited by systemic pretreatment with MK-801. Our findings demonstrate that NMDA receptors and nNOS mediate the tachycardiac response to dynamic exercise, possibly through an NMDA receptor-NO signaling mechanism. However, NMDA receptors, but not nNOS, mediate the exercise-evoked pressor response. The present results also provide evidence that MPFC, BNST and PAG may modulate physiological adjustments during dynamic exercise through NMDA receptor-NO signaling. © 2013 Elsevier B.V.

Interaction between fiscal and monetary policy in a dynamic nonlinear model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An experimental nonlinear low dynamic stiffness device for shock isolation

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements. Copyright (C) 2015 Elsevier Ltd. All rights reserved

Cardiovascular responses to dynamic exercise with acute anemia in humans

[EN] We hypothesized that reducing arterial O2 content (CaO2) by lowering the hemoglobin concentration ([Hb]) would result in a higher blood flow, as observed with a low PO2, and maintenance of O2 delivery. Seven young healthy men were studied twice, at rest and during two-legged submaximal and peak dynamic knee extensor exercise in a control condition (mean control [Hb] 144 g/l) and after 1-1.5 liters of whole blood had been withdrawn and replaced with albumin [mean drop in [Hb] 29 g/l (range 19-38 g/l); low [Hb]]. Limb blood flow (LBF) was higher (P < 0.01) with low [Hb] during submaximal exercise (i.e., at 30 W, LBF was 2.5 +/- 0.1 and 3.0 +/- 0.1 l/min for control [Hb] and low [Hb], respectively; P < 0.01), resulting in a maintained O2 delivery and O2 uptake for a given workload. However, at peak exercise, LBF was unaltered (6.5 +/- 0.4 and 6.6 +/- 0.6 l/min for control [Hb] and low [Hb], respectively), which resulted in an 18% reduction in O2 delivery (P < 0.01). This occurred despite peak cardiac output in neither condition reaching >75% of maximal cardiac output (approximately 26 l/min). It is concluded that a low CaO2 induces an elevation in submaximal muscle blood flow and that O2 delivery to contracting muscles is tightly regulated.

Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup

Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone's material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of thirteen femora predicted the strength (R2=0.84, SEE=540 N, 16.2%), stiffness (R2=0.82, SEE=233 N/mm, 18.0%) and fracture energy (R2=0.72, SEE=3.85 J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation.