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 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.

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 Analisis Kestabilan dan Keuntungan Maksimum Model Predator-Prey Fungsi Respon Tipe Holling III dengan Usaha Pemanenan

2018 ◽  
Author(s):  
DIDIHARYONO DIDIHARYONO
Keyword(s):  
Equilibrium Point ◽  
Linearization Method ◽  
Stability Test ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Type Iii ◽  
Hurwitz Stability ◽  
Predator Prey Model ◽  
Maximum Profit ◽  
Prey Model

In this paper, we discussed stability analysis of predator-prey model with Holling type III and will harvesting effort at second populations. The research aimed is, to investigate solution the predator-prey model with Holling type III functional response with addition harvesting effort and to investigate maximum profit from optimal harvesting at second populations. Stability of equilibrium point use linearization method and determine the stability by notice the eigenvalues of Jacoby matrix evaluation of equilibrium point and can also be determined using Hurwitz stability test by observing the coefficients of the characteristic equation. The result shows that the obtained an interior point 〖TE〗_2^* (x^*,y^*) which asymptotic stable according to Hurwitz stability test and find maximum profit of exploitation effort or harvest at second populations. Predator-prey population is always exist in their life, although exploitation with harvesting effort and given maximum profit is π_max=162.68 where to find maximum profit on critical points of surface profit function.

scholarly journals Stability analysis of two predators and one prey population model with harvesting in fisheries management

2021 ◽  
Vol 921 (1) ◽  
pp. 012005
Author(s):  
D Didiharyono ◽  
S Toaha ◽  
J Kusuma ◽  
Kasbawati
Keyword(s):  
Equilibrium Point ◽  
Population Model ◽  
Fishery Management ◽  
Stable Equilibrium ◽  
Prey Population ◽  
Positive Equilibrium ◽  
Stable Equilibrium Point ◽  
Maximum Profit ◽  
Positive Equilibrium Point ◽  
Prey Populations

Abstract The discussion is focussed in the interaction between two predators and one prey population model in fishery management. Mathematically model is built by involving harvesting with constant efforts in the two predators and one prey populations. The positive equilibrium point of the model is analyzed via linearization and Routh-Hurwitz stability criteria. From the analysis, there exists a certain condition that makes the positive equilibrium point is asymptotically stable. The stable equilibrium point is then related to the maximum profit problem. With suitable value of harvesting efforts, the maximum profit is reached and the predator and prey populations remain stable. Finally, a numerical simulation is carried out to find out how much the maximum profit is obtained and to visualize how the trajectories of predator and prey tend to the stable equilibrium point.

Hopf Bifurcation and Stability Analysis for a Predator-Prey Model with Delays

2013 ◽  
Vol 850-851 ◽  
pp. 901-904
Author(s):  
Hong Bing Chen ◽  
Li Mei Wang
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Critical Value ◽  
Stable Equilibrium Point ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Necessary And Sufficient ◽  
Bifurcation And Stability

In this paper, a predatorprey model with discrete and distributed delays is investigated. The necessary and sufficient of the stable equilibrium point for this model is studied. Further, analyzed the associated characteristic equation. And, it is found that Hopf bifurcation occurs when τ crosses some critical value. Last, an example showed the feasibility of results.

scholarly journals Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

2017 ◽  
Vol 27 (1) ◽  
pp. 91-103 ◽  
Author(s):  
H.A. Kruthika ◽  
Arun D. Mahindrakar ◽  
Ramkrishna Pasumarthy
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Cancer Immunotherapy ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Delay Systems ◽  
Long Term Outcome ◽  
Predator Prey ◽  
Gene Regulatory

Abstract In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov–Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator–prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator–prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.

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.

Sign in / Sign up

Export Citation Format

Share Document