Valuing Potential Benefits of Research into the Biological Control of Californian Thistle （Cirsium arvense）： A Bioeconomic Model

The present research developed a bioeconomic model for control of Californian thistle （Cirsium arvense L. Scop.） in intensive, lowland sheep pastures in New Zealand. Production costs included two control methods： herbicides and defoliation, with defoliation encompassing both physical means and biocontrol measures. The model was used to examine the economic value of a research programme into biological control of the weed, given several different future scenarios. These scenarios were high herbicide prices, a price premium for lamb raised without chemical herbicides, and development of herbicide resistance. The model results were used to estimate national impacts. If the only change in the agricultural sector was the cost of the biocontrol to the nation＇s farmers, the research programme to find an effective biocontrol agent had little economic impact. If other factors changed, such as the price of petroleum or levels of herbicide resistance in the weed. the model＇s results suggested that intensive sheep farming could grow or shrink by as much as NZ$219 million dollars over five years. In the latter case, having an alternative control method reduced potential losses and increased potential gains, resulting in a net benefit of between NZ$81 million and NZ$153 million. This work extended prior research in several ways. First. Californian thistle reproduces via root buds, which affected the modelling of weed behaviour. Secondly, the model allowed optimistation over continuous levels of weed control for two different methods. Thirdly, the model accounted for both weed control and damage to nitrogen-fixing clover from herbicide use. Finally, the research investigated optimal weed control in several different alternative future states.

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic interest.We firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation phenomenon.Next,we introduce a st ate feedback controller to elimina te the singularity induced bifurcation phenomenon,and discuss the optimal control problems.Finally,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

Land degradation, government subsidy, and smallholders＇ conservation decision： the case of the loess plateau in China

Land degradation is one of the severe environmental problems in China. In order to combat land degradation, a soil conservation program was introduced since 2000 to reduce soil erosion by converting slope-cultivated land into forestry and pasture. This paper represents the first systematic attempt to investigate the impact of the soil conservation program on land degradation in the loess plateau. The results indicate that the soil conservation program to convert slope fields into forest or pasture is an effective way to combat soil erosion. However, a subsidy that is higher than profit of land use activity of slope fields before their conversion into forest and pasture is needed to encourage farmers to join the conservation program. A policy measure to encourage and assist farmers to develop sedentary livestock by using crops produced from fields as well as fodder and forage grass from the converted slope fields might contribute to combat soil erosion. Increase in off-farm job opportunities may encourage households to reduce cultivation in slope fields. That implies a policy measure to encourage rural urbanization might contribute to combat soil erosion.

A SINGULAR BIOECONOMIC MODEL WITH DIFFUSION AND TIME DELAY

This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena： Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.