A Mathematical Modelling Approach for a Past-Dependent Prey-Predator System

A memory dependent prey-predator model incorporating Allee effect in prey is analysed. For a small and high values of memory rate, the dynamical changes in the prey and predator densities are demonstrated. The equilibria of the proposed model and the local stability analysis corresponding to each equilibrium are presented. The variables of prey and predator species with respect to memory rate are investigated and the existence of the Hopf bifurcation is shown. The analytical part of this paper is supported with detailed numerical simulations

APPLICATION OF THE KALMAN FILTER ON FULL TENSOR GRAVITY GRADIOMETRY DATA AROUND THE VINTON SALT DOME, LOUISIANA

Full tensor gravity (FTG) data are known for their high resolution but also for higher noise in its components due to the dynamic nature of the platform used for data acquisition. Although a review of the literature suggests steady increase in the success of gravity gradiometry, we still cannot take advantage of the full potential of the method, mostly because of the noise with the same amplitude and wavenumber characteristics as the signal that affects these data. Smoothing from common low pass filters removes small wavelength features and makes it difficult to detect structural features and other density variations of interest to exploration. In Kalman filtering the components of the FTG are continuously updated to calculate the best estimation of the state. The most important advantage of the Kalman filter is that it can be applied on gravity gradiometry components simultaneously. In addition, one can incorporate constraints. We use the Laplace’s equation that is the most meaningful constraint for potential field data to extract signal from noise and improve the detection and continuity of density variations. We apply the Kalman filter on the FTG data acquired by Bell Geospace over the Vinton salt dome in southwest Louisiana

A Mathematical Study on the Dynamics of an Eco-Epidemiological Model in the Presence of Delay

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical simulations are carried out to explain our theoretical analysis

Host-Parasite Arms Races and Rapid Changes in Bird Egg Appearance

Abstract Coevolutionary arms races are a powerful force driving evolution, adaptation, and diversification. They can generate phenotypic polymorphisms that render it harder for a coevolving parasite or predator to exploit any one individual of a given species. In birds, egg polymorphisms should be an effective defense against mimetic brood parasites and are extreme in the African tawny-flanked prinia (Prinia subflava) and its parasite, the cuckoo finch (Anomalospiza imberbis). Here we use models of avian visual perception to analyze the appearance of prinia and cuckoo finch eggs from the same location over 40 years. We show that the two interacting populations have experienced rapid changes in egg traits. Egg colors of both species have diversified over time, expanding into avian color space as expected under negative frequency-dependent selection. Egg pattern showed signatures of both frequency-dependent and directional selection in different traits, which appeared to be evolving independently of one ano..