Spatiotemporal Dynamics of Phytoplankton-Fish System with the Allee Effect and Harvest Effect

2013 ◽  
Vol 726-731 ◽  
pp. 1604-1610
Author(s):  
Wei Wei Zhang ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Pattern Formation ◽  
Equilibrium Point ◽  
Allee Effect ◽  
Spatiotemporal Dynamics ◽  
The Stability ◽  
Fish Interactions

In this paper, spatiotemporal dynamics of a phytoplankton-fish system with the Allee effect and harvest effect are investigated mathematically and numerically. Mathematical theoretical works have been pursued for the investigation of the stability of the equilibrium point of the phytoplankton-fish system with the Allee effect and harvest effect, which in turn provide a theoretical basic for the numerical simulation. Numerical analysis works indicate that Allee effect and harvest effect have a strong effect on the spatiotemporal dynamics of the phytoplankton-fish system using pattern formation. These results may help us to better understand phytoplankton-fish interactions.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

On the Dynamical Behavior of Three Species System with Time Delays

2011 ◽  
Vol 130-134 ◽  
pp. 1544-1546
Author(s):  
Dan Na Sun ◽  
Zi Ku Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Zero Point ◽  
The Stability ◽  
Population Equilibrium

A three species system with time delays was considered. Firstly, we got the system’s three population equilibrium point and shifted it to zero point through transformation. Secondly, we analyzed the stability of the system at the equilibrium point. We support our analytical findings with numerical simulation.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Peng Feng
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Functional Response ◽  
Allee Effect ◽  
Turing Instability ◽  
Spatial Pattern Formation ◽  
The Stability ◽  
Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

scholarly journals Pattern Formation in a Bacterial Colony Model

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xinze Lian ◽  
Guichen Lu ◽  
Hailing Wang
Keyword(s):  
Stability Analysis ◽  
Pattern Formation ◽  
Time Evolution ◽  
Real World ◽  
Spatiotemporal Dynamics ◽  
Bacterial Colony ◽  
Numerical Evidence ◽  
Diffusion Controlled ◽  
Model Dynamics ◽  
The Stability

We investigate the spatiotemporal dynamics of a bacterial colony model. Based on the stability analysis, we derive the conditions for Hopf and Turing bifurcations. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by parameters in the model and find that the model dynamics exhibit a diffusion controlled formation growth to spots, holes and stripes pattern replication, which show that the bacterial colony model is useful in revealing the spatial predation dynamics in the real world.

scholarly journals On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2235
Author(s):  
Sameh Askar
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Utility Function ◽  
Global Analysis ◽  
Asymmetric Structure ◽  
Two Dimensional ◽  
Cournot Duopoly ◽  
The Stability ◽  
Nash Point ◽  
Discrete Map

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

scholarly journals Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors

2020 ◽  
Vol 17 (1) ◽  
pp. 50-60
Author(s):  
Nursamsi Nursamsi
Keyword(s):  
Diabetes Mellitus ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Immune Function ◽  
Blood Sugar ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Sugar Levels ◽  
The Stability

Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

scholarly journals Dynamic Analysis and Chaos Control of Bertrand Triopoly Based on Differentiated Products and Heterogeneous Expectations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Liuwei Zhao
Keyword(s):  
Dynamical System ◽  
Numerical Analysis ◽  
Equilibrium Point ◽  
Economic System ◽  
Dynamic Behavior ◽  
Game Model ◽  
Complex Dynamic ◽  
Heterogeneous Expectations ◽  
Price Game ◽  
The Stability

Price competition has become a universal commercial phenomenon nowadays. This paper considers a dynamic Bertrand price game model, in which enterprises have heterogeneous expectations. By the stability theory of the dynamic behavior of the Bertrand price game model, the instability of the boundary equilibrium point and the stability condition of the internal equilibrium point are obtained. Furthermore, bifurcation diagram, basin of attraction, and critical curve are introduced to investigate the dynamic behavior of this game. Numerical analysis shows that the change of model parameters in a dynamic system has a significant impact on the stability of the system and can even lead to complex dynamic behaviors in the evolution of the entire economic system. This kind of complex dynamic behavior will cause certain damage to the stability of the whole economic system, causing the market to fall into a chaotic state, which is manifested as a kind of market disorder competition, which is very unfavorable to the stability of the economic system. Therefore, the chaotic behavior of the dynamical system is controlled by time-delay feedback control and the numerical analysis shows that the effective control of the dynamical system can be unstable behavior and the rapid recovery of the market can be stable and orderly.

scholarly journals Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Liu ◽  
Yong Ye ◽  
Yumei Wei ◽  
Weiyuan Ma ◽  
Ming Ma ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Point Of View ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pattern Formations

In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations.

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