Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem

We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting.

Baseline Plant-to-Plant Larval Movement of Spodoptera eridania in Bt and Non-Bt Soybean and Its Possible Impacts on IRM

The widespread use of transgenic technologies has led to the emergence of insect populations resistant to Bt toxins. Some lepidopteran pest species also appear to naturally have some level of tolerance to certain proteins, such as some species of Spodoptera to Cry1Ac. One of the main strategies to manage resistance is the use of refuge areas, the success of which is in part dependent on larval movement of the target pest. Thus, in order to assess the viability of a refuge strategy addressing Spodoptera eridania Stoll (Lepidoptera: Noctuidae) in Bt soybean, it was evaluated the larval movement across plants in Bt and non-Bt soybean, as well as the larval development and mortality on Bt and non-Bt soybean cultivars. We concluded that apparent S. eridania incomplete resistance resulting from high larval mortality and low adaptability on Bt plants, high larval dispersal, nondirectional larval movement, and random larval spatial dispersion suggest that structured refuge is more suitable than mixed refuge for managing resistance in S. eridania populations.

DYNAMIC BEHAVIOR OF PREDATOR-PREY WITH RATIO DEPENDENT, REFUGE IN PREY AND HARVEST FROM PREDATOR

<span class="fontstyle0">Abstract </span><span class="fontstyle2">In this paper, we discuss a dynamical behavior of Predator-Prey with ratio<br />dependent, refuge in prey, and harvest from predator. Model reconstruction is<br />organized by adding the refuge control in prey with the values </span><span class="fontstyle3">0 </span><span class="fontstyle4"> </span><span class="fontstyle5">m </span><span class="fontstyle4"> </span><span class="fontstyle3">1, </span><span class="fontstyle2">and linear<br />predator harvesting. The aim of analysis is to describe the equilibrium points and<br />their stability. In analysis, the possible fixed points are the prey extinction, the<br />predator extinction, and predator-prey coexists. By using linearization, the<br />stability of predator extinction point is unstable, and the prey extinction point,<br />coexists point becomes stable with certain condition. Finally, the dynamical<br />simulation show that the trajectories of solution convergent to their stability, and<br />the refuge strategy suitable to avoid the extinction of prey.<br /></span><span class="fontstyle0">Key Word</span><span class="fontstyle6">: Dynamic Behavior, Predator-Prey, Predation, Refuges, Harvest</span> <br /><br />

The Corn–Cotton Agroecosystem in the Mid-Southern United States: What Insecticidal Event Pyramids Should be Used in Each Crop to Extend Vip3A Durability

Recent studies suggest that resistance in Helicoverpa zea (Boddie) (Lepidoptera, Noctuidae) to Cry1A(b/c) and Cry2Ab2 toxins from the bacterium Bacillus thuringiensis Berliner (Bacillales: Bacillaceae) has increased and field efficacy is impacted in transgenic corn and cotton expressing these toxins. A third toxin, Vip3A, is available in pyramids expressing two or more Bt toxins in corn hybrids and cotton varieties, but uncertainty exists regarding deployment strategies. During a growing season, H. zea infests corn and cotton, and debate arises over use of Vip3A toxin in corn where H. zea is not an economic pest. We used a three-locus, spatially explicit simulation model to evaluate when using Vip3A in corn might hasten evolution of resistance to Vip3A, with implications in cotton where H. zea is a key pest. When using a conventional refuge in corn and initial resistance allele frequencies of Cry1A and Cry2A were 10%, transforming corn with Vip3A slowed resistance to these toxins and delayed resistance evolution to the three-toxin pyramid as a whole. When Cry resistance allele frequencies exceeded 30%, transforming corn with Vip3A hastened the evolution of resistance to the three-toxin pyramid in cotton. When using a seed blend refuge strategy, resistance was delayed longest when Vip3A was not incorporated into corn and used only in cotton. Simulations of conventional refuges were generally more durable than seed blends, even when 75% of the required refuge was not planted. Extended durability of conventional refuges compared to other models of resistance evolution are discussed as well as causes for unusual survivorship in seed blends.