A NUMERICAL STUDY ON PREDATOR PREY MODEL

2012 ◽  
Vol 09 ◽  
pp. 347-353
Author(s):  
MOHAMED FARIS LAHAM ◽  
ISTHRINAYAGY KRISHNARAJAH ◽  
ABDUL KADIR JUMAAT
Keyword(s):  
Stochastic Processes ◽  
Numerical Study ◽  
Spatial Models ◽  
Euler Method ◽  
Volterra Model ◽  
Population Cycle ◽  
Stochastic Representation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Spatial Models

Stochastic spatial models are becoming a popular tool for understand the ecological and evolution of ecosystem problems. We consider the predator prey interactions in term of stochastic representation of this Lotka-Volterra model and explore the use of stochastic processes to extinction behavior of the interacting populations. Here, we present simulation of stochastic processes of continuous time Lotka-Volterra model. Euler method has been used to solve the predator prey system. The trajectory spiral graph has been plotted based on obtained solution to show the population cycle of predator as a function of time.

Pattern Formation Controlled by External Forcing in a Spatial Harvesting Predator-Prey Model

2011 ◽  
pp. 214-221
Author(s):  
Feng Rao
Keyword(s):  
Reaction Diffusion ◽  
Euler Method ◽  
External Forcing ◽  
Periodic Forcing ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Flux Boundary Conditions ◽  
Predator Prey Models ◽  
The Stability

Predator–prey models in ecology serve a variety of purposes, which range from illustrating a scientific concept to representing a complex natural phenomenon. Due to the complexity and variability of the environment, the dynamic behavior obtained from existing predator–prey models often deviates from reality. Many factors remain to be considered, such as external forcing, harvesting and so on. In this chapter, we study a spatial version of the Ivlev-type predator-prey model that includes reaction-diffusion, external periodic forcing, and constant harvesting rate on prey. Using this model, we study how external periodic forcing affects the stability of predator-prey coexistence equilibrium. The results of spatial pattern analysis of the Ivlev-type predator-prey model with zero-flux boundary conditions, based on the Euler method and via numerical simulations in MATLAB, show that the model generates rich dynamics. Our results reveal that modeling by reaction-diffusion equations with external periodic forcing and nonzero constant prey harvesting could be used to make general predictions regarding predator-prey equilibrium,which may be used to guide management practice, and to provide a basis for the development of statistical tools and testable hypotheses.

scholarly journals Periodicity and Permanence of a Discrete Impulsive Lotka-Volterra Predator-Prey Model Concerning Integrated Pest Management

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Chang Tan ◽  
Jun Cao
Keyword(s):  
Discrete System ◽  
Numerical Experiments ◽  
Critical Value ◽  
Euler Method ◽  
Impulsive Effect ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

By piecewise Euler method, a discrete Lotka-Volterra predator-prey model with impulsive effect at fixed moment is proposed and investigated. By using Floquets theorem, we show that a globally asymptotically stable pest-eradication periodic solution exists when the impulsive period is less than some critical value. Further, we prove that the discrete system is permanence if the impulsive period is larger than some critical value. Finally, some numerical experiments are given.

scholarly journals Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hui Zhang ◽  
Zhihui Ma ◽  
Gongnan Xie ◽  
Lukun Jia
Keyword(s):  
Time Scale ◽  
Stable State ◽  
Volterra Model ◽  
Fast Time ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction ◽  
Game Dynamic

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.

MODELING OF BIOLOGICAL POPULATIONS USING FUZZY DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 09 ◽  
pp. 354-363 ◽  
Author(s):  
M. Z. AHMAD ◽  
M. K. HASAN
Keyword(s):  
Differential Equations ◽  
Phase Plane ◽  
Fuzzy Model ◽  
Euler Method ◽  
Numerical Results ◽  
Predator Prey ◽  
New Model ◽  
Predator Prey Model ◽  
The Stability ◽  
Over Time

This paper explores the application of fuzzy differential equations in modeling of prey and predator populations. A new model, referred to as fuzzy predator-prey model is introduced. This model is then solved numerically by means of a fuzzy Euler method. Some numerical results are presented in order to show the evolution of the prey and predator populations over time. Finally, the stability of the new fuzzy model is studied and shown graphically in the fuzzy phase plane.

scholarly journals Economic and Mathematical Model for Size and Structure Optimisation of Predator and Prey Populations

2019 ◽  
Vol 8 (4) ◽  
pp. 9081-9090
Keyword(s):  
Mathematical Model ◽  
Animal Species ◽  
Volterra Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Vito Volterra ◽  
Size And Structure ◽  
Prey Populations

The paper proposes an original economic and mathematical model for size and structure optimisation of Predator and Prey populations. The most well-known mathematical model in biology for periodical dynamics of antagonistic animal species was developed independently by Alfred Lotka and Vito Volterra. This classical mathematical Predator-Prey model is known as the Lotka-Volterra model.

scholarly journals APPLICATION OF THE “PREDATOR-PREY” MODEL FOR ANALYSIS AND FORECASTING THE SHARE OF THE MARKET OF MOBILE OPERATING SYSTEMS

2019 ◽  
pp. 3-11
Author(s):  
Olena Nikolaieva ◽  
Yevheniia Bochko
Keyword(s):  
Market Share ◽  
Operating Systems ◽  
Dynamic Systems ◽  
Optimization Problem ◽  
Statistical Data ◽  
Volterra Model ◽  
System Of Differential Equations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Special Points

The study is aimed to analyze the dynamic behavior of indicators of the market share of operating systems of mobile devices using the modified Lotka-Volterra model. Using the solution of an optimization problem, the coefficients of a system of differential equations in the case of two and three competitors are estimated on the basis of real statistical data, and special points and properties of data from dynamic systems are investigated. Based on the numerical integration of the obtained equations, predictions are made of the market share of mobile operating systems Android and iOS.

A NOTE ON SDRE CONTROL APPLIED IN PREDATOR–PREY MODEL: BIOLOGICAL CONTROL OF SPIDER MITE PANONYCHUS ULMI

2016 ◽  
Vol 24 (02n03) ◽  
pp. 333-344 ◽  
Author(s):  
ANGELO MARCELO TUSSET ◽  
VINÍCIUS PICCIRILLO ◽  
JOSE MANOEL BALTHAZAR
Keyword(s):  
Spider Mite ◽  
Critical Concentration ◽  
State Feedback Control ◽  
Panonychus Ulmi ◽  
Volterra Model ◽  
Control Technique ◽  
Economic Damage ◽  
Predator Prey ◽  
Predator Prey Model ◽  
State Dependent

The spider mite Panonychus ulmi (P. ulmi) is one of the most important pests of apple plantations. Studies suggested that spider mite Neoseiulus californicus (N. californicus) is able to control spider mite P. Ulmi, minimizing the risk of having leaves with high index of injury, therefore avoiding economic damage. In this work, we consider a predator–prey system, where the prey is the mite P. ulmi and its predator is the spider mite N. californicus. The coefficients for the Lotka–Volterra model with competition between predators are obtained. Here, we will use the state-dependent riccati equation (SDRE) control technique to design a state feedback control, and to determine a state observer. In both cases, it is necessary to solve the quadratic optimal control problem for nonlinear systems. Numerical simulations shown that both approaches are efficient to stabilize the system in a desired point below the critical concentration, allowing us to minimize the level of economic damage.

scholarly journals A Predator-Prey Model In Deterministic And Stochastic Environments

2021 ◽  
Author(s):  
Chandra P. Limbu
Keyword(s):  
Numerical Simulations ◽  
Ecological Systems ◽  
Volterra Model ◽  
Phase Portraits ◽  
Hopf Bifurcations ◽  
Stochastic Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Environments ◽  
Uniqueness Of Limit Cycles

We investigate the phase portraits, the uniqueness of limit cycles and the Hopf bifurcations in the Holling-Tanner models in deterministic and stochastic environments. We provide the conditions on the parameters to assure saddle, focus and node. We use numerical simulations to demonstrate our results in the deterministic cases. We also explore the Holling-Tanner model in a stochastic environment by using numerical simulations. We generalize and improve some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems.

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