Competition and Predation Models

2021 ◽  
pp. 61-84
Author(s):  
Timothy E. Essington
Keyword(s):  
Stability Analysis ◽  
Model System ◽  
Basic Principles ◽  
Model Stability ◽  
Predator Prey ◽  
Interacting Species ◽  
Analytical Stability ◽  
Stable Equilibria ◽  
Mathematical Equations ◽  
Predict Model

The chapter “Competition and Predation Models” considers models with two or more interacting species. What needs to happen for there to be “stable equilibria” that contain all possible members of a system? This is where simple models can be useful: these interactions can be represented by mathematical equations, and then solved for conditions that allow species to coexist. This chapter shows three techniques that make it possible to take a model system and determine whether the system has a stable equilibrium with all members present. The basic principles of model stability are presented, as well as how mathematical models can be used to address basic ecological questions in competition and predator-prey systems. Isocline analysis and analytical stability analysis are explained as ways to predict model behavior and are then used to draw inferences about the processes acting in the real world.

scholarly journals Stability Analysis and Harvesting Effort Predator Prey Populations Model Holling Type III with Maximum Profit

2021 ◽  
Author(s):  
Didiharyono D.
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Profit Function ◽  
Model Stability ◽  
Predator Prey ◽  
Type Iii ◽  
Hurwitz Stability ◽  
Maximum Profit ◽  
Asymptotic Stable ◽  
Prey Populations

In this paper discussed stability analysis and harvesting effort at second predator prey populations model Holling type III with maximum profit. The step this research is to determine the equilibrium point, linearize the model, stability analysis of the equilibrium point, and numerical simulation. Result shows that obtained an interior point T𝐸2∗(𝑁1∗,𝑁2∗) that asymptotic stable based on Hurwitz stability test then obtained maximum profit from exploitation harvesting effort of second predator prey populations. This second populations will always exist, even though exploited with harvesting effort done by humans. Harvesting effort of second predator-prey populations given maximum profit (𝜋𝑚𝑎𝑥) that occur on critical points of surface profit function

scholarly journals Analisis Kestabilan dan Usaha Pemanenan Model Predator Prey Tipe Holling III dengan Keuntungan Maksimum

Jurnal Varian ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 55-61
Author(s):  
Didiharyono Didiharyono ◽  
Muh Irwan
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Profit Function ◽  
Model Stability ◽  
Predator Prey ◽  
Numerical Simulation Result ◽  
Hurwitz Stability ◽  
Maximum Profit ◽  
Asymptotic Stable ◽  
Prey Populations

In this paper discussed Stability Analysis and Harvesting Effort at second Predator Prey Populations model Holling Type III with Maximum Profit. The step this research is to determine the equilibrium point, linearize the model, stability analysis of the equilibrium point, and numerical simulation. Result shows that obtained an interior point T  that asymptotic stable based on Hurwitz stability test then obtained maximum profit from exploitation harvesting effort of second predator prey populations. This second populations will always exist, even though exploited with harvesting effort done by humans. Harvesting effort of second predator-prey populations given maximum profit  that occur on critical points of surface profit function

scholarly journals Stability Analysis and Harvesting Effort Predator Prey Populations Model Holling Type III with Maximum Profit

2019 ◽  
Author(s):  
Bahtiar
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Profit Function ◽  
Model Stability ◽  
Predator Prey ◽  
Type Iii ◽  
Hurwitz Stability ◽  
Maximum Profit ◽  
Asymptotic Stable ◽  
Prey Populations

In this paper discussed Stability Analysis and Harvesting Effort at second Predator Prey Populations model Holling Type III with Maximum Profit. The step this research is to determine the equilibrium point, linearize the model, stability analysis of the equilibrium point, and numerical simulation. Result shows that obtained an interior point TE_2^* (N_1^*,N_2^* ) that asymptotic stable based on Hurwitz stability test then obtained maximum profit from exploitation harvesting effort of second predator prey populations. This second populations will always exist, even though exploited with harvesting effort done by humans. Harvesting effort of second predator-prey populations given maximum profit 〖(π〗_max) that occur on critical points of surface profit function.

Tristability of thin orthotropic shells with uniform initial curvature

2008 ◽  
Vol 464 (2099) ◽  
pp. 2949-2966 ◽  
Author(s):  
S Vidoli ◽  
C Maurini
Keyword(s):  
Stability Analysis ◽  
Stable Equilibrium ◽  
Initial Shape ◽  
Analytical Stability ◽  
Degeneracy Condition ◽  
Equilibrium Configurations ◽  
Wide Range ◽  
Numerical Stability Analysis ◽  
Stable Equilibria ◽  
Orthotropic Shells

Composite shells show a rich multistable behaviour of interest for the design of shape-changing (morphing) structures. Previous studies have investigated how the initial shape determines the shell stability properties. For uniform initial curvatures and orthotropic material behaviour, not more than two stable equilibria have been reported. In this paper, we prove that untwisted, uniformly curved, thin orthotropic shells can have up to three stable equilibrium configurations. Cases of tristability are first documented using a numerical stability analysis of an extensible shallow shell model. Including mid-plane extension shows that the shells must be sufficiently curved in relation to their thickness to be multistable. Thus, an inextensible model allows us to perform an analytical stability analysis. Focusing on untwisted initial configurations, we illustrate with simple analytical results how the material parameters of the shell control the dependence of its multistable behaviour on the initial curvatures. In particular, we show that when the bending stiffness matrix approaches a degeneracy condition, the shell exhibits three stable equilibria for a wide range of initial curvatures.

Turing Stability Analysis in a Reaction-Diffusion Predator-Prey System with Fear Effect

2021 ◽  
Author(s):  
Gong Chen ◽  
Min Xiao ◽  
Shi Chen ◽  
Shuai Zhou ◽  
Yunxiang Lu ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Predator Prey ◽  
Fear Effect ◽  
Prey System
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