MULTIPLE SPATIAL SCALE ANALYSIS OF WHOOPING CRANE HABITAT IN NEBRASKA

Geographic Information System (GIS) and remote sensing technologies were used to evaluate whooping crane stopover habitat in Nebraska. The goal of the research was to investigate habitat selection at multiple spatial scales. The GIS database consisted of all confirmed whooping crane sightings reported in Nebraska from 1975-1996 and land cover information delineated from color infrared aerial photographs and Landsat Thematic Mapper data. Results suggest that whooping cranes select roost habitat by recognizing site-level and landscape-scale land cover composition. Wetland is the most strongly selected habitat type at all spatial scales examined. This presentation emphasizes methods used to analyze habitat selection and how the information can be applied in conservation

Population Trends of Quails in North America

We used North American Breeding Bird Survey data (1966-91) to estimate distribution, relative abundance, and population trends of quails. Population trends in grassland/shrub birds sympatric with northern bobwhite (Colinus virginianus) were also examined. Northern bobwhite and scaled quail (Callipepl,a squamata) populations have declined since 1966. Rates of decline for these quails have increased during the past decade. California quail (C. califomica), Gambel\u27s quail (C. gambelii), and mountain quail (Oreortyx pictus) populations have been stable over the long-term (1966-91). However, the short-term (1982-91) trend for California quail is positive, whereas Gambel\u27s quail appear to be declining. Patterns in trends indicate similar factors may be negatively affecting breeding populations of grassland/shrub birds throughout the bobwhite\u27s range. We discuss plausible hypotheses to explain population trends and recommend future action

Invariant manifold theory for impulsive functional differential equations with applications

The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous dynamical systems framework. We prove a variation-of-constants formula, introduce appropriate generalizations of stable, centre and unstable subspaces, and develop a Floquet theory for periodic systems. Using the Lyapunov-Perron method, we prove the existence of local centre manifolds at a nonhyperbolic equilibrium of nonlinear impulsive functional differential equations. Using a formal differentiation procedure in conjunction with machinery from functional analysis -- specifically, contraction mappings on scales of Banach spaces -- we prove that the centre manifold is smooth in the state space. By introducing a coordinate system, we are able to prove that the coefficients of any Taylor expansion of the local centre manifold are unique and sufficiently regular in the time and lag arguments that they can be computed by solving an impulsive boundary-value problem. After proving a reduction principle, this leads naturally to explorations into bifurcation theory, where we establish generalizations of the classical fold and Hopf bifurcations for impulsive delay differential equations. Aside from the centre manifold, we demonstrate the existence and smoothness of stable and unstable manifolds and prove a linearized stability theorem. One of the applications of the theory above is an analysis of a SIR model with pulsed vaccination and finite temporary immunity modeled by a discrete delay. We determine an analytical stability criteria for the disease-free equilibrium and prove the existence of a transcritical bifurcation of periodic solutions at some critical vaccination coverage level for generic system parameters. Then, using numerical continuation and a monodromy operator discretization scheme, we track the bifurcating endemic periodic solution until a Hopf point is identifed. A cylinder bifurcation is observed; the periodic orbit expands into a cylinder in the extended phase space before eventually contracting onto a periodic orbit as the vaccination coverage vanishes. The other application is an impulsive stabilization method based on centre manifold reduction and optimization principles. Assuming a cost structure on the impulsive controller and a desired convergence rate target, we prove that under certain conditions there is always an impulsive controller that can stabilize a nonhyperbolic equilibrium with a trivial unstable subspace, robustly with respect to parameter perturbation, while guaranteeing a minimal cost. We then exploit the low-dimensionality of the centre manifold to develop a two-stage program that can be implemented to compute the optimal controller. To demonstrate the effectiveness of the two-stage program, which we call the centre probe method, we use the method to stabilize a complex network of 100 diffusively coupled nodes at a Hopf point. The cost structure is one that assigns higher cost to controlling of nodes that have more neighbours, while the jump functionals are required to be diagonal -- that is, they do not introduce further coupling. We also introduce a secondary goal, which is that the number of nodes that are controlled is minimized

Habitat and Weather Effects on Northern Bobwhite Brood Movements

We observed radio-marked northern bobwhite (Colinus virginianus) broods (adults with chicks :S21 days old; n = 12) in Kansas during 1991-94 to test effects of weather (temperature and precipitation) and macrohabitat (composition, relative diversity, and mean distance to grassland) variables on brood home range size and daily movements at large (28.5 km2), intermediate (3.14 km2), and small (about 0.14 km2) spatial scales surrounding habitats available for broods. Principal component analyses followed by stepwise multiple linear regression indicated neither weather nor habitat influenced (P 2: 0.1) home range size at the large and intermediate scales. However, the principal component representing mean distance to grassland and percent cropland within the home range (i.e., at a small scale) was positively related to home range size. Neither temperature nor habitat influenced daily distance of movements. We concluded that brood mobility was independent of landscape-scale features, but that habitat management at smaller spatial scales could influence movements. To create optimal habitat for bobwhite, managers should consider relationships among habitat attributes and the movement of individuals, including the spatial scales at which these relationships are most important

Worrisome Properties of Neural Network Controllers and Their Symbolic Representations

We raise concerns about controllers' robustness in simple reinforcement learning benchmark problems. We focus on neural network controllers and their low neuron and symbolic abstractions. A typical controller reaching high mean return values still generates an abundance of persistent low-return solutions, which is a highly undesirable property, easily exploitable by an adversary. We find that the simpler controllers admit more persistent bad solutions. We provide an algorithm for a systematic robustness study and prove existence of persistent solutions and, in some cases, periodic orbits, using a computer-assisted proof methodology.Comment: accepted to ECAI2

Bifurcation of Bounded Solutions of Impulsive Differential Equations

Electronic version of an article published as International Journal of Bifurcation and Chaos, Volume 26, No. 14, 2016, 1-20 doi:10.1142/S0218127416502424 © copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218127416502424In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results