scholarly journals Refuge and Age Structures Impact on the Bifurcation Analysis of an Ecological Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Azhar Abbas Majeed
Keyword(s):  
Functional Response ◽  
Bifurcation Analysis ◽  
Ecological Model ◽  
Equilibrium Points ◽  
Single Point ◽  
Pitchfork Bifurcation ◽  
Local Bifurcation ◽  
Symmetry Point ◽  
Volterra Type ◽  
The Stability

In this paper, the conditions of the incidence of the local bifurcation, such as a saddle-node pitchfork bifurcation and transcritical of an ecological system (consistingprey shelter (refuge) and age stages for both populations) considered to study. Lotka-Volterra type of functional response was suggested. Subsequently, the inquiry and analysis are remarked that the transcritical bifurcation transpires close to the equilibrium(symmetry) point , in addition to the incidence of asaddle-node bifurcation at symmetry points and . It should be mentioned that there is no likelihood of the incidence of the pitchfork bifurcation at every single point. In conclusion,s to illustrate the incidence of the local bifurcation of this system, some simulations were used. The aim of this study is to examine the effect of each parameter on the stability of equilibrium points.

scholarly journals The Dynamics of A Square Root Prey-Predator Model with Fear

2020 ◽  
pp. 139-146
Author(s):  
Nabaa Hassain Fakhry ◽  
Raid Kamel Naji
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Square Root ◽  
Predator Species ◽  
Local Bifurcation Analysis ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

Stability and Bifurcation Analysis of an Asymmetrically Electrostatically Actuated Microbeam

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Hadi Madinei ◽  
Ghader Rezazadeh ◽  
Saber Azizi
Keyword(s):  
Applied Voltage ◽  
Equilibrium Points ◽  
Pitchfork Bifurcation ◽  
Spring Model ◽  
Electrostatically Actuated ◽  
Proposed Model ◽  
Mass Spring Model ◽  
The Stability ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper deals with the study of bifurcational behavior of a capacitive microbeam actuated by asymmetrically located electrodes in the upper and lower sides of the microbeam. A distributed and a modified two degree of freedom (DOF) mass–spring model have been implemented for the analysis of the microbeam behavior. Fixed or equilibrium points of the microbeam have been obtained and have been shown that with variation of the applied voltage as a control parameter the number of equilibrium points is changed. The stability of the fixed points has been investigated by Jacobian matrix of system in the two DOF mass–spring model. Pull-in or critical values of the applied voltage leading to qualitative changes in the microbeam behavior have been obtained and has been shown that the proposed model has a tendency to a static instability by undergoing a pitchfork bifurcation whereas classic capacitive microbeams cease to have stability by undergoing to a saddle node bifurcation.

scholarly journals The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Raid Kamel Naji ◽  
Reem Mudar Hussien
Keyword(s):  
Infectious Diseases ◽  
Vertical Transmission ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Host Population ◽  
Local Bifurcation ◽  
Local Bifurcation Analysis ◽  
Different Types

An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction numberR0is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four-dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

Stability and Bifurcation Analysis in a Nonlinear Harvested Predator–Prey Model with Simplified Holling Type IV Functional Response

2020 ◽  
Vol 30 (14) ◽  
pp. 2050205
Author(s):  
Zuchong Shang ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Jun Miao
Keyword(s):  
Functional Response ◽  
Limit Cycle ◽  
Bifurcation Analysis ◽  
Homoclinic Loop ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Prey Model ◽  
The Stability ◽  
Parameter Values

In this paper, a type of predator–prey model with simplified Holling type IV functional response is improved by adding the nonlinear Michaelis–Menten type prey harvesting to explore the dynamics of the predator–prey system. Firstly, the conditions for the existence of different equilibria are analyzed, and the stability of possible equilibria is investigated to predict the final state of the system. Secondly, bifurcation behaviors of this system are explored, and it is found that saddle-node and transcritical bifurcations occur on the condition of some parameter values using Sotomayor’s theorem; the first Lyapunov constant is computed to determine the stability of the bifurcated limit cycle of Hopf bifurcation; repelling and attracting Bogdanov–Takens bifurcation of codimension 2 is explored by calculating the universal unfolding near the cusp based on two-parameter bifurcation analysis theorem, and hence there are different parameter values for which the model has a limit cycle, or a homoclinic loop; it is also predicted that the heteroclinic bifurcation may occur as the parameter values vary by analyzing the isoclinic of the improved system. Finally, numerical simulations are done to verify the theoretical analysis.

scholarly journals Bridging theories for ecosystem stability through structural sensitivity analysis of ecological models in equilibrium

2019 ◽  
Author(s):  
Jan J. Kuiper ◽  
Bob W. Kooi ◽  
Garry D. Peterson ◽  
Wolf M. Mooij
Keyword(s):  
Food Web ◽  
Functional Response ◽  
Species Interactions ◽  
Linear Functional ◽  
Regime Shift ◽  
Equilibrium Points ◽  
Interaction Terms ◽  
Structural Sensitivity Analysis ◽  
Shift Dynamics ◽  
The Stability

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from a different angle. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths from observations. Models of regime shifts focus on qualitative changes of equilibrium points in a slowly changing environment, and typically include non-linear functional response terms. Currently, it is unclear how the stability of an empirical food web model, expressed as the rate of system recovery after a small perturbation, relates to the vulnerability of the ecosystem to collapse. Here, we conduct structural sensitive analyses of classical consumer-resource models in equilibrium along an environmental gradient. Specifically, we change non-proportional interaction terms into linear ones, while maintaining the equilibrium biomass densities and flux of matter, to analyze how alternative model formulations shape the stability properties of the equilibria. The results reveal no consistent relationship between the stability of the original models and the linearized versions, even though they describe the same biomass values and material flows. We use these findings to discuss whether stability analysis of observed equilibria by empirical food web models can provide insight into regime shift dynamics, and highlight the challenge of bridging alternative modelling approaches in ecology and beyond.

scholarly journals Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Haiyun Bi ◽  
Guoyuan Qi ◽  
Jianbing Hu
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Controller Design ◽  
Structural Parameters ◽  
Equilibrium Points ◽  
Pitchfork Bifurcation ◽  
Stable Node ◽  
Modeling And Analysis ◽  
Chaotic Region ◽  
Aerial Vehicle ◽  
The Stability

A model of the attitude system for a quadrotor unmanned aerial vehicle (QUAV), assumed to be a rigid body, is developed. For specific parameter configurations, a chaotic region with a saddle and two stable node-focus equilibrium points is identified. The chaotic model provides an important reference for dynamic analysis and a challengeable task of controller design once the flight enters the chaotic region of parameters. The pitchfork bifurcation of the equilibrium points is provided. Rich dynamics of the system are revealed by two bifurcation regions, which demonstrates the diversity of the flight behaviors as the parameters vary. One bifurcation analysis is with respect to the speed of the front propeller and the speed difference of the front and left propellers, and another one is with respect to the speed of the front propeller and moment of inertia. The dynamic characteristics of the QUAV are further verified by the Casimir power bifurcations. The trajectories of three settings with different structural parameters are analyzed in detail. The stability of the QUAV is found to be enhanced for certain optimized values of the structural parameters. Finally, using the Casimir power and Lagrange multiplier method, a supremum bound of the chaotic attractor is presented.

Hopf Bifurcation Analysis in a Modified Optically Injected Semiconductor Lasers Model

2014 ◽  
Vol 631-632 ◽  
pp. 254-260
Author(s):  
Jiang Ang Zhang ◽  
Wen Ju Du ◽  
Kutorzi Edwin Yao
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Semiconductor Lasers ◽  
Bifurcation Analysis ◽  
Autonomous System ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Bifurcation Parameter ◽  
Numerical Example ◽  
The Stability

In this paper, a modified optically injected semiconductor lasers model is studied in detail. More precisely, we study the stability of the equilibrium points and basic dynamic properties of the autonomous system by means of nonlinear dynamics theory. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the stability and the conditions for generating Hopf bifurcation of the equilibria are derived. Then, a numerical example is given.

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