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

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

Impact of different bioenergy crops on area allocation and cellulosic ethanol feedstock mix

Although a cellulosic ethanol mandate for 2022 is in place, significant political, economic, and agronomic uncertainty exists surrounding the attainability of the mandate. This paper evaluates the effects of bioenergy crop yield and cost uncertainty on land allocation and the feedstock mix for cellulosic ethanol in the United States. The county-level model focuses on corn, soybeans, and wheat as the field crops and corn stover, wheat straw, switchgrass, and miscanthus as the biomass feedstocks. The economic model allocates land optimally among the alternative crops given a binding cellulosic biofuel mandate. The model is calibrated to 2022 in terms of yield, crop demand, and baseline prices. The bioenergy and commodity prices resulting from a mandate are endogenous to the model. The scenarios simulated differ in terms of bioenergy crop types (switchgrass and miscanthus), bioenergy crop yields, bioenergy production cost, and the cellulosic biofuel mandate ranging from 15 to 60 billion gallons. Our results indicate that the largest proportion of agricultural land dedicated to either switchgrass or miscanthus is found in the Southern Plains and the Southeast. Almost no bioenergy crops are grown in the Midwest across all scenarios. The 15 and 30 billion liter mandates in the high production cost scenarios for switchgrass and in all miscanthus scenarios are covered to 95\% by agricultural residues. Changes in the prices for the three commodities are negligible for low cellulosic ethanol mandates because most of the mandate is met with agricultural residues. The amount of bioenergy crops brought into production at the highest imposed mandate result in price increases ranging from 5% for corn and soybeans to almost 14% for wheat

Co-firing in Coal Power Plants and its Impact on Biomass Feedstock Availability

Several states have a renewable portfolio standard (RPS) and allow for biomass co-firing to meet the RPS requirements. In addition, a federal renewable fuel standard (RFS) mandates an increase in cellulosic ethanol production over the next decade. This paper quantifies the effects on local biomass supply and demand of different co-firing policies imposed on 398 existing coal-fired power plants. Our model indicates which counties are most likely to be able to sustain cellulosic ethanol plants in addition to co-firing electric utilities. The simulation incorporates the county-level biomass market of corn stover, wheat straw, switchgrass, and forest residues as well as endogenous crop prices. Our scenarios indicate that there is sufficient feedstock availability in Southern Minnesota, Iowa, and Central Illinois. Significant supply shortages are observed in Eastern Ohio, Western Pennsylvania, and the tri-state area of Illinois, Indiana, and Kentucky which are characterized by a high density of coal-fired power plants with high energy output

Impact of agronomic uncertainty in biomass production and endogenous commodity prices on cellulosic biofuel feedstock composition

This study evaluates the effect of agronomic uncertainty on bioenergy crop production as well as endogenous commodity and biomass prices on the feedstock composition of cellulosic biofuels under a binding mandate in the United States. The county-level simulation model focuses on both field crops (corn, soybean, and wheat) and biomass feedstocks (corn stover, wheat straw, switchgrass, and Miscanthus). In addition, pasture serves as a potential area for bioenergy crop production. The economic model is calibrated to 2022 in terms of yield, crop demand, and baseline prices and allocates land optimally among the alternative crops given the binding cellulosic biofuel mandate. The simulation scenarios differ in terms of bioenergy crop type (switchgrass and Miscanthus) and yield, biomass production inputs, and pasture availability. The cellulosic biofuel mandates range from 15 to 60 billion L. The results indicate that the 15 and 30 billion L mandates in the high production input scenarios for switchgrass and Miscanthus are covered entirely by agricultural residues. With the exception of the low production input for Miscanthus scenario, the share of agricultural residues is always over 50% for all other scenarios including the 60 billion L mandate. The largest proportion of agricultural land dedicated to either switchgrass or Miscanthus is found in the southern Plains and the southeast. Almost no bioenergy crops are grown in the Midwest across all scenarios. Changes in the prices for the three commodities are negligible for cellulosic ethanol mandates because most of the mandate is met with agricultural residues. The lessons learned are that (1) the share of agricultural residue in the feedstock mix is higher than previously estimated and (2) for a given mandate, the feedstock composition is relatively stable with the exception of one scenario

The effects of uncertainty under a cap-and-trade policy on afforestation in the United States

To combat climate change, cap-and-trade policies have been proposed and implemented in countries around the world. The stochastic carbon price that results from a cap-and-trade policy makes investment decisions in carbon mitigating and sequestering practices more complex. This letter illustrates the consequence of uncertainty by analyzing forest carbon offset credits under a potential cap-and-trade policy in the United States. The effects of uncertainty on afforestation, carbon sequestration, cropland allocation, and commodity prices using a real option framework are assessed. When compared with deterministic models, less land gets converted from cropland to forestry over the projection period of 40 years because landowners find it optimal to wait before changing land-use to gain more information about the carbon price evolution. The simulation shows that most afforestation occurs in the south and the northeast with almost no conversion in the Corn Belt. The lesson for policy makers is that under carbon price uncertainty, lower afforestation and carbon sequestration takes place. To foster afforestation, mechanisms are necessary to reduce uncertainty at the expense of higher commodity prices

Canard-like phenomena in piecewise-smooth Van der Pol systems

We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard solutions and explosion in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards ``with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation---whether leading to canards or super-explosion---can be subcritical.Comment: 17 pages, 11 figure