scholarly journals Modeling the Dynamics of Predator-Prey Community with Age Structures

2019 ◽  
Vol 14 (1) ◽  
pp. 77-93 ◽  
Author(s):  
G.P. Neverova ◽  
O.L. Zhdanova ◽  
E.Ya. Frisman
Keyword(s):  
Numerical Study ◽  
Classical Model ◽  
Interaction Coefficient ◽  
Individual Development ◽  
Dynamic Mode ◽  
Population Fluctuations ◽  
Predator Prey ◽  
Sustainable Community Development ◽  
Periodic Dynamics ◽  
The Stability

A model of the predator-prey community has been proposed with specific stages of individual development and the seasonality of breeding processes. It is assumed each of the species has an age structure with two stages of development. The case typical for the community “Arctic fox – rodents” is modeled. An analytical and numerical study of the model proposed is made. It is shown that periodic, quasi-periodic and chaotic oscillations can occur in the system, as well as a shift in the dynamics mode as a result of changes in the current sizes of the community’s populations. The model proposed demonstrates long-period oscillations with time delay like auto-oscillations in the classical model of Lotka-Volterra. It is shown that a transition from stable dynamics to quasi-periodic oscillations and vise verse is possible in the system, while an increase in the values of the half capturing saturation coefficient reduces the possibility of quasiperiodic oscillation emergence. Simulations demonstrate the growth in predator’s consumption of the prey average number expands the zones of multistability and quasi-periodic dynamics in the stability area of nontrivial fixed point. Therefore, the variation of the current population size of the community can lead to a change in the dynamic mode observed. The scenarios of transition from stationary dynamics to community’s population fluctuations are analyzed with different values of population parameters determining the dynamics of both species and their interaction coefficient. The model shows both sustainable community development and various complex fluctuations of interacting species. At the same time, the prey dynamics affects the predator one: the prey population fluctuations initiate predator oscillations like prey’s fluctuations, while the intrapopulation parameters of the predator can give to both stationary and fluctuating dynamic modes.

scholarly journals Mutual inductance instability of the tip vortices behind a wind turbine

2014 ◽  
Vol 755 ◽  
pp. 705-731 ◽  
Author(s):  
Sasan Sarmast ◽  
Reza Dadfar ◽  
Robert F. Mikkelsen ◽  
Philipp Schlatter ◽  
Stefan Ivanell ◽  
...  
Keyword(s):  
Growth Rate ◽  
Wind Turbine ◽  
Numerical Study ◽  
Operating Conditions ◽  
Analytical Relationship ◽  
Dynamic Mode ◽  
Spatial Structures ◽  
Tip Vortices ◽  
Positive Growth ◽  
The Stability

AbstractTwo modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier–Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tjæreborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120° symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360° wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\pi /2$ and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

Numerical and Experimental Analysis of a Hybrid Wind-Wave Offshore Floating Platform’s Hull

2018 ◽  
Author(s):  
Thiago S. Hallak ◽  
José F. Gaspar ◽  
Mojtaba Kamarlouei ◽  
Miguel Calvário ◽  
Mário J. G. C. Mendes ◽  
...  
Keyword(s):  
Wave Energy ◽  
Experimental Analysis ◽  
Wind Wave ◽  
Numerical Study ◽  
Energy Devices ◽  
Wave Energy Converters ◽  
Wave Basin ◽  
Hybrid Concept ◽  
Point Absorbers ◽  
The Stability

This paper presents a study regarding a novel hybrid concept for both wind and wave energy offshore. The concept resembles a semi-submersible wind platform with a larger number of columns. Wave Energy Devices such as point absorbers are to be displayed around the unit, capturing wave energy while heaving and also enhancing the stability of the platform. In this paper, a first numerical study of the platform’s hull, without Wave Energy Converters, is carried out. Experiments in wave basin regarding the same unit have been conducted and the results are presented and compared to the numerical ones. Both stability and seakeeping performances are assessed and compared.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Étude de la réouverture de la lagune du Havre aux Basques. I. Modélisation numérique des conditions d'écoulement

1995 ◽  
Vol 22 (1) ◽  
pp. 55-71
Author(s):  
Y. Ouellet ◽  
A. Khelifa ◽  
J.-F. Bellemare
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Element Model ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Modélisation Numérique ◽  
Tidal Flows ◽  
Dimensional Finite Element ◽  
The Stability ◽  
La Madeleine

A numerical study based on a two-dimensional finite element model has been conducted to analyze flow conditions associated with different possible designs for the reopening of Havre aux Basques lagoon, located in Îles de la Madeleine, in the middle of the Gulf of St. Lawrence. More specifically, the study has been done to better define the depth and geometry of the future channel as well as its orientation with regard to tidal flows within the inlet and the lagoon. Results obtained from the model have been compared and analyzed to put forward some recommendations about choice of a design insuring the stability of the inlet with tidal flows. Key words: numerical model, finite element, lagoon, reopening, Havre aux Basques, Îles de la Madeleine.

Impact of Predator Signals on the Stability of a Predator–Prey System: A Z-Control Approach

2018 ◽  
Author(s):  
Sk Shahid Nadim ◽  
Sudip Samanta ◽  
Nikhil Pal ◽  
Ibrahim M. ELmojtaba ◽  
Indranil Mukhopadhyay ◽  
...  
Keyword(s):  
Predator Prey ◽  
Control Approach ◽  
System A ◽  
Prey System ◽  
The Stability ◽  
Predator Signals
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