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.

scholarly journals Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chunqing Wu ◽  
Shengming Fan ◽  
Patricia J. Y. Wong
Keyword(s):  
Sufficient Conditions ◽  
Theoretical Studies ◽  
Patchy Environment ◽  
Predator Prey ◽  
Numerical Examples ◽  
Predator Prey Model ◽  
Prey Model ◽  
Dispersal Corridors ◽  
Predator Prey Models ◽  
Theoretical Results

We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey models. By comparing the two permanence criteria, we discuss the effects of dispersal corridors on the permanence of the predator-prey model. It is found that the dispersion of the prey from one patch to another is helpful to the permanence of the prey if the population growth of the prey is density dependent; however, this dispersion of the prey could be disadvantageous or advantageous to the permanence of the predator. Five numerical examples are presented to confirm the theoretical results obtained and to illustrate the effects of dispersal corridors on the permanence of the predator-prey model.

First U-Pb dating of fossilized soft tissue using a new approach to paleontological chronometry

Geology ◽  
2021 ◽  
Author(s):  
Heriberto Rochín-Bañaga ◽  
Donald W. Davis ◽  
Tobias Schwennicke
Keyword(s):  
Soft Tissue ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Uranium Content ◽  
New Approach ◽  
Inductively Coupled ◽  
Shark Teeth ◽  
Inductively Coupled Mass Spectrometry ◽  
Late Diagenesis ◽  
Three Dimensional Space

Previous U-Pb dating of fossils has had only limited success because of low uranium content and abundance of common Pb as well as element mobility during late diagenesis. We report the first accurate U-Pb dating of fossilized soft tissue from a Pliocene phosphatized bivalve mold using laser ablation–inductively coupled mass spectrometry (LA-ICPMS). The fossilized soft tissue yields a diagenetic U-Pb age of 3.16 ± 0.08 Ma, which is consistent with its late Pliocene stratigraphy and similar to the oldest U-Pb age measured on accompanying shark teeth. Phosphate extraclasts give a distinctly older age of 5.1 ± 1.7 Ma, indicating that they are likely detrital and may have furnished P, promoting phosphatization of the mold. The U-Pb ages reported here along with stratigraphic constraints suggest that diagenesis occurred shortly after the death of the bivalve and that the U-Pb system in the bivalve mold remained closed until the present. Shark teeth collected from the same horizon show variable resetting due to late diagenesis. Data were acquired as line scans in order to exploit the maximum Pb/U variation and were regressed as counts, rather than ratios, in three-dimensional space using a Bayesian statistical method.

scholarly journals Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shuang Guo ◽  
Weihua Jiang
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Normal Form Method ◽  
Predator Prey Models ◽  
The Stability

A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.

Dynamic Simulation of Multibody Mechanical Systems Using the Vector-Network Model

1988 ◽  
Vol 12 (1) ◽  
pp. 21-30 ◽  
Author(s):  
M.J. Richard
Keyword(s):  
Dynamic Models ◽  
Analytical Procedure ◽  
Dimensional Space ◽  
Digital Simulation ◽  
Three Dimensional ◽  
General Purpose ◽  
New Approach ◽  
Network Method ◽  
Definition Of ◽  
Three Dimensional Space

Pressing technological problems have created a growing interest in the development of dynamic models for the digital simulation of multibody systems. This paper describes a new approach to the problem of motion prediction. An extension of the “vector-network” method to rigid body systems in three-dimensional space is introduced. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics are combined. The analytical procedure was successfully implemented within a general-purpose digital simulation program since, from a minimal definition of the mechanism, it will automatically predict the behavior of the system as output, thereby giving the impression that the equations governing the motion of the mechanical system have been completely formulated and solved by the computer. Simulations of the response of a rail vehicle which demonstrate the validity, applicability and self-formulating aspect of the automated model are provided.

From 5-SS Platform Linkage to Four-Revolute Jointed Planar, Spherical and Bennett Mechanisms

2016 ◽  
Author(s):  
Xin Ge ◽  
A. Purwar ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Examples ◽  
Revolute Joints ◽  
Novel Approach ◽  
Design Variables ◽  
Moving Points ◽  
Unified Algorithm ◽  
Three Dimensional Space

Recently, we developed a novel approach to the problem of geometric design of 5-SS platform linkages such that its moving points are constrained on a sphere or a plane. Dual quaternions are used to obtain the bilinear design equations with seven design variables, which can be further recast into a linear equation with 16 design variables with a set of simple proportional relationships. This leads to a novel algorithm that reduces the kinematic design problem to that of null space analysis followed by a generalized eigenvalue problem. In this paper, we show that the same approach leads to a unified algorithm for synthesizing planar, spherical and spatial Bennet mechanisms with four revolute joints as over-constrained four-revolute jointed mechanisms in three dimensional space. Numerical examples are given in the end.

scholarly journals Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response

2020 ◽  
Vol 99 (99) ◽  
pp. 1-12
Author(s):  
Yinshu Wu ◽  
Wenzhang Huang
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models ◽  
Global And Local

A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses.

scholarly journals New Approach for Solving Three Dimensional Space Partial Differential Equation

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0786 ◽  
Author(s):  
Enadi Et al.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Partial Differential ◽  
Transform Method ◽  
New Approach ◽  
Practical Implications ◽  
Three Dimensional Space

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.        Finally, all algorithms in this paper are implemented in MATLAB version 7.12.

scholarly journals Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shuang Guo ◽  
Weihua Jiang
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Three Dimensional ◽  
Growth Time ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
System With Time Delay

A class of three-dimensional Gause-type predator-prey model is considered. Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system (2005), to give the global stability of the equilibrium. Secondly, we analyze the stability of coexisting equilibrium of predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.

Design of 3-Dimensional Guidance Law of Missile Based on Discrete Sliding Mode

2013 ◽  
Vol 816-817 ◽  
pp. 976-980
Author(s):  
Nuan Wen ◽  
Zheng Hua Liu ◽  
Le Chang
Keyword(s):  
Discrete Time ◽  
Relative Motion ◽  
Sliding Mode ◽  
Dimensional Space ◽  
Three Dimensional ◽  
New Approach ◽  
3 Dimensional ◽  
Guidance Law ◽  
Guidance Laws ◽  
Three Dimensional Space

In this article, a new approach to design discrete-time sliding-mode guidance laws is presented based on the target-missile relative motion equation in three-dimensional space. This method significantly reduced system chattering and could be easily achieved on engineering. Furthermore, effectiveness of the proposed guidance laws is demonstrated through simulation by comparing with the traditional proportional guidance laws.

A Multicolor Grid Technique for Volumetric Velocity Measurements

2017 ◽  
Author(s):  
Kadeem Dennis ◽  
Kamran Siddiqui
Keyword(s):  
Light Beam ◽  
Turbulent Flows ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Beam Width ◽  
Field Of View ◽  
New Approach ◽  
Grid Technique ◽  
Color Combinations ◽  
Three Dimensional Space

Turbulent flows are three-dimensional by nature. A major challenge in turbulence research is the simultaneous measurement of all three velocity components in three-dimensional space. Recently, Rainbow Volumic Velocimetry (RVV) has emerged as a promising technique to visualize and measure three-dimensional flow fields. The RVV technique projects a multicolor light beam in the measurement region. Currently, the technique utilizes beam color variations in one plane i.e. perpendicular to the camera field of view but is restricted to small measurement volumes. In this paper, a new approach of light beam projection using a multicolor grid is proposed that allows beam color variations in multiple planes relative to the camera field of view. This enables the extension of the light beam width through multiple color combinations. Details of the technique and its implementation are presented along with the preliminary results that demonstrates the viability of this technique.

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