scholarly journals Analysis of Structure-Preserving Discrete Models for Predator-Prey Systems with Anomalous Diffusion

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1172 ◽  
Author(s):  
Joel Alba-Pérez ◽  
Jorge E. Macías-Díaz
Keyword(s):  
Anomalous Diffusion ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Continuous Model ◽  
Discrete Models ◽  
Extended Form ◽  
Original Population ◽  
Predator Prey ◽  
Structure Preserving ◽  
Spatial Dimensions

In this work, we investigate numerically a system of partial differential equations that describes the interactions between populations of predators and preys. The system considers the effects of anomalous diffusion and generalized Michaelis–Menten-type reactions. For the sake of generality, we consider an extended form of that system in various spatial dimensions and propose two finite-difference methods to approximate its solutions. Both methodologies are presented in alternative forms to facilitate their analyses and computer implementations. We show that both schemes are structure-preserving techniques, in the sense that they can keep the positive and bounded character of the computational approximations. This is in agreement with the relevant solutions of the original population model. Moreover, we prove rigorously that the schemes are consistent discretizations of the generalized continuous model and that they are stable and convergent. The methodologies were implemented efficiently using MATLAB. Some computer simulations are provided for illustration purposes. In particular, we use our schemes in the investigation of complex patterns in some two- and three-dimensional predator–prey systems with anomalous diffusion.

scholarly journals A New Approach to Global Stability of Discrete Lotka-Volterra Predator-Prey Models

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Young-Hee Kim ◽  
Sangmok Choo
Keyword(s):  
Global Stability ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Discrete Models ◽  
New Approach ◽  
Predator Prey ◽  
Numerical Examples ◽  
Predator Prey Model ◽  
Predator Prey Models ◽  
Three Dimensional Space

An Euler difference scheme for a three-dimensional predator-prey model is considered and we introduce a new approach to show the global stability of the scheme. For this purpose, we partition the three-dimensional space and calculate the sign of the rate change of population of species in each partitioned region. Our method is independent of dimension and then can be applicable to other dimensional discrete models. Numerical examples are presented to verify the results in this paper.

Three-dimensional predator–prey interactions: a computer simulation of bird flocks and aircraft

1986 ◽  
Vol 64 (11) ◽  
pp. 2624-2633 ◽  
Author(s):  
Peter F. Major ◽  
Lawrence M. Dill ◽  
David M. Eaves
Keyword(s):  
Computer Simulation ◽  
Prey Species ◽  
Three Dimensional ◽  
Aircraft Engine ◽  
Aquatic Environments ◽  
Aircraft Engines ◽  
Predator Prey ◽  
Simulation Techniques ◽  
Computer Simulation Techniques ◽  
Individual Prey

Three-dimensional interactions between grouped aerial predators (frontal discs of aircraft engines), either linearly arrayed or clustered, and flocks of small birds were studied using interactive computer simulation techniques. Each predator modelled was orders of magnitude larger than an individual prey, but the prey flock was larger than each predator. Expected numbers of individual prey captured from flocks were determined for various predator speeds and trajectories, flock–predator initial distances and angles, and flock sizes, shapes, densities, trajectories, and speeds. Generally, larger predators and clustered predators caught more prey. The simulation techniques employed in this study may also prove useful in studies of predator–prey interactions between schools or swarms of small aquatic prey species and their much larger vertebrate predators, such as mysticete cetaceans.The study also provides a method to study problems associated with turbine aircraft engine damage caused by the ingestion of small flocking birds, as well as net sampling of organisms in open aquatic environments.

scholarly journals Targets, ripples and spirals in a precipitation system with anomalous dispersion

2015 ◽  
Vol 17 (30) ◽  
pp. 19806-19814 ◽  
Author(s):  
Mahmoud M. Ayass ◽  
Istvan Lagzi ◽  
Mazen Al-Ghoul
Keyword(s):  
Anomalous Diffusion ◽  
Heterogeneous System ◽  
Three Dimensional ◽  
Anomalous Dispersion ◽  
Precipitation System ◽  
Wave Phenomena ◽  
Dimensional Wave

We report multiple three-dimensional wave phenomena in a heterogeneous system due to anomalous diffusion.

scholarly journals Celestial Spheres

2018 ◽  
Vol 2 (2) ◽  
pp. 168-186
Author(s):  
Austin M. Freeman
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Good Evidence ◽  
Medieval Period ◽  
The Bible ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
Modern Physics ◽  
The Subject ◽  
Three Dimensional Space

Angels probably have bodies. There is no good evidence (biblical, philosophical, or historical) to argue against their bodiliness; there is an abundance of evidence (biblical, philosophical, historical) that makes the case for angelic bodies. After surveying biblical texts alleged to demonstrate angelic incorporeality, the discussion moves to examine patristic, medieval, and some modern figures on the subject. In short, before the High Medieval period belief in angelic bodies was the norm, and afterwards it is the exception. A brief foray into modern physics and higher spatial dimensions (termed “hyperspace”), coupled with an analogical use of Edwin Abbott’s Flatland, serves to explain the way in which appealing to higher-dimensional angelic bodies matches the record of angelic activity in the Bible remarkably well. This position also cuts through a historical equivocation on the question of angelic embodiment. Angels do have bodies, but they are bodies very unlike our own. They do not have bodies in any three-dimensional space we can observe, but are nevertheless embodied beings.

Solving two-point seismic-ray tracing problems in a heterogeneous medium

1980 ◽  
Vol 70 (1) ◽  
pp. 79-99 ◽  
Author(s):  
V. Pereyra ◽  
W. H. K. Lee ◽  
H. B. Keller
Keyword(s):  
Numerical Method ◽  
Ray Tracing ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Nonlinear Boundary Conditions ◽  
Variable Order ◽  
Flexible Tool ◽  
Velocity Models ◽  
Jump Discontinuities ◽  
Variable Mesh

abstract A study of two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically will be presented in a series of papers. In this Part 1, it is shown how a variety of two-point seismic-ray tracing problems can be formulated mathematically as systems of first-order nonlinear ordinary differential equations subject to nonlinear boundary conditions. A general numerical method to solve such systems in general is presented and a computer program based upon it is described. High accuracy and efficiency are achieved by using variable order finite difference methods on nonuniform meshes which are selected automatically by the program as the computation proceeds. The variable mesh technique adapts itself to the particular problem at hand, producing more detailed computations where they are needed, as in tracing highly curved seismic rays. A complete package of programs has been produced which use this method to solve two- and three-dimensional ray-tracing problems for continuous or piecewise continuous media, with the velocity of propagation given either analytically or only at a finite number of points. These programs are all based on the same core program, PASVA3, and therefore provide a compact and flexible tool for attacking ray-tracing problems in seismology. In Part 2 of this work, the numerical method is applied to two- and three-dimensional velocity models, including models with jump discontinuities across interfaces.

scholarly journals Positive Solutions of a Diffusive Predator-Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoqing Wen ◽  
Yue Chen ◽  
Hongwei Yin
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Disease Spread ◽  
Dimensional System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fixed Point Index Theory

We study a three-dimensional system of a diffusive predator-prey model including disease spread for prey and with Dirichlet boundary condition and Michaelis-Menten functional response. By semigroup method, we are able to achieve existence of a global solution of this system. Extinction of this system is established by spectral method. By using bifurcation theory and fixed point index theory, we obtain existence and nonexistence of inhomogeneous positive solutions of this system in steady state.

scholarly journals An Exceptionally Preserved Three-Dimensional Armored Dinosaur Reveals Insights into Coloration and Cretaceous Predator-Prey Dynamics

2017 ◽  
Vol 27 (16) ◽  
pp. 2514-2521.e3 ◽  
Author(s):  
Caleb M. Brown ◽  
Donald M. Henderson ◽  
Jakob Vinther ◽  
Ian Fletcher ◽  
Ainara Sistiaga ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Predator Prey

Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices

2019 ◽  
Vol 25 (2) ◽  
pp. 475-497
Author(s):  
Vincent Picandet ◽  
Noël Challamel
Keyword(s):  
Difference Equations ◽  
Differential Operators ◽  
Scale Effects ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Continuous Model ◽  
Lattice System ◽  
Discrete Problem ◽  
Linear Difference Equations ◽  
One Dimensional

The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

scholarly journals Nonlinear interaction between self- and parametrically excited wind-induced vibrations

2020 ◽  
Author(s):  
Simona Di Nino ◽  
Angelo Luongo
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Continuous Model ◽  
Galerkin Projection ◽  
Bifurcation Equation ◽  
Static Theory ◽  
Dimensional Parameter ◽  
Harmonic Perturbation ◽  
Sample Structure

AbstractThe aeroelastic behavior of a planar prismatic visco-elastic structure, subject to a turbulent wind, flowing orthogonally to its plane, is studied in the nonlinear field. The steady component of wind is responsible for a Hopf bifurcation occurring at a threshold critical value; the turbulent component, which is assumed to be a small harmonic perturbation of the former, is responsible for parametric excitation. The interaction between the two bifurcations is studied in a three-dimensional parameter space, made of the two wind amplitudes and the frequency of the turbulence. Aeroelastic forces are computed by the quasi-static theory. A one-D.O.F dynamical system, drawn by a Galerkin projection of the continuous model, is adopted. The multiple scale method is applied, to get a two-dimensional bifurcation equation. A linear stability analysis is carried out to determine the loci of periodic and quasi-periodic bifurcations. Limit cycles and tori are computed by exact, asymptotic, and numerical solutions of the bifurcation equations. Numerical results are obtained for a sample structure, and compared with finite-difference solutions of the original partial differential equation of motion.

Sign in / Sign up

Export Citation Format

Share Document