Bifurcation-based parameter tuning in a model of the GnRH pulse and surge generator

We investigate a model of the GnRH pulse and surge generator, with the definite aim of constraining the model GnRH output with respect to a physiologically relevant list of specifications. The alternating pulse and surge pattern of secretion results from the interaction between a GnRH secreting system and a regulating system exhibiting fast-slow dynamics. The mechanisms underlying the behavior of the model are reminded from the study of the Boundary-Layer System according to the "dissection method" principle. Using singular perturbation theory, we describe the sequence of bifurcations undergone by the regulating (FitzHugh-Nagumo) system, encompassing the rarely investigated case of homoclinic connexion. Basing on pure dynamical considerations, we restrict the space of parameter search for the regulating system and describe a foliation of this restricted space, whose leaves define constant duration ratios between the surge and the pulsatility phase in the whole system. We propose an algorithm to fix the parameter values to also meet the other prescribed ratios dealing with amplitude and frequency features of the secretion signal. We finally apply these results to illustrate the dynamics of GnRH secretion in the ovine species and the rhesus monkey

Fold-Saddle Bifurcation in Non-Smooth Vector Fields on the Plane

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three parameter families of a class of Non-Smooth Vector Fields are studied and its bifurcation diagrams are exhibited. Our main result describes the unfolding of the so called Fold-Saddle singularity

On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four

Sensitivity of Carbon Emission Estimates from Indirect Land-Use Change

We analyze the sensitivity of greenhouse gas (GHG) emissions from land-use change to modifications in assumptions concerning crop area, yield, and deforestation. For this purpose, we run a modified version of the Center for Agricultural and Rural Development (CARD) Agricultural Outlook Model, which was used previously to assess the impacts of energy price increases and biofuel policy changes on land conversion. To calculate the GHG implications of agricultural activity, we use GreenAgSiM, a model developed to evaluate emissions from land conversion and agricultural production. Both models are applied to scenarios that lead to higher US ethanol production. The results are contrasted with the findings of Searchinger et al., and we explain the role of model assumptions to elucidate the differences. We find that the payback period of corn ethanol’s carbon debt is sensitive to assumptions concerning land conversion and yield growth and can range from 31 to 180 years.biofuel, crop yield, greenhouse gas emissions, indirect land-use change.

The Influence of Trust and Attitudes on the Purchase Frequency of Organic Produce

Growth in organic food sales is mainly due to consumers becoming more aware of health issues and environmental concerns. Understanding the drivers of organic consumption is crucial to predict future market outcomes. In this analysis, the authors expand previous research by including general and institutional trust variables in addition to consumer attitudes to examine organic food purchases. Food production is unobservable and hence, consumers need to exhibit trust with respect to organic production and certification. A bivariate ordered probit model applied to U.S. survey data confirms that organic purchases are determined by health, nutrition, and taste. In some cases, general trust and trust in media are statistically significant. Trust in institutions that are involved in the organic certification process is not statistically significant. A hierarchical cluster analysis grouping consumers based on trust and attitudes shows that (dis)trust in the organic certification and supply chain does not hinder organic food market growth

Some results on homoclinic and heteroclinic connections in planar systems

Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set ${\Phi(n,b)=0}.$ The method is applied to two quadratic families, one of them is the well-known Bogdanov-Takens system. One of the results that we obtain for this system is the bifurcation curve for small values of $n$, given by $b=\frac5 7 n^{1/2}+{72/2401}n- {30024/45294865}n^{3/2}- {2352961656/11108339166925} n^2+O(n^{5/2})$. We obtain the new three terms from purely algebraic calculations, without evaluating Melnikov functions

On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review

Producing energy while sequestering carbon? The relationship between biochar and agricultural productivity

A partial solution to problems associated with anthropogenic greenhouse gas (GHG) emissions could be the development and deployment of carbon-negative technologies, i.e., producing energy while reducing atmospheric carbon dioxide levels. Biofuels have been considered a possibility but have faced limitations due to competition with food production and GHG emissions through indirect land-use change (ILUC). In this article, we show how emissions from ILUC can potentially be reduced by producing food and bioenergy from biochar amended soils. The possibility of yield improvements from biochar would reduce the land requirement for crop production and thus, lead to a reduction in emissions from ILUC. In our application, biochar and bio-oil are produced via fast pyrolysis of corn stover. Bio-oil is subsequently upgraded into a fuel suitable for use in internal combustion engines. Applying the U.S. regulatory method used to determine biofuel life cycle emissions, our results show that a biochar-induced yield improvement in the U.S. Midwest ranging from 1% to 8% above trend can lead to an ILUC credit between 1.65 and 14.79 t CO2-equivalent ha−1 year−1 when future emissions are assessed over the next 30 years. The model is generalizable to other feedstocks and locations and illustrates the relationship between biochar and crop production