scholarly journals Investigating Lotka-Volterra model using computer simulation

2020 ◽  
Vol 3 (10) ◽  
Author(s):  
F. Kunis ◽  
M. Dimitrov
Keyword(s):  
Computer Simulation ◽  
Population Dynamics ◽  
Numerical Solution ◽  
Fourth Order ◽  
Real Data ◽  
Volterra Model ◽  
Predator Prey ◽  
Prey System ◽  
Two Populations ◽  
Over Time

In this project we study the Lotka-Volterra model, also known as the model describing the population dynamics in the Predator-prey system. This model describes the interaction of the two species and also the development of their populations over time. We simulate this model using the fourth-order Runge-Kutta algorithm. This is the most widely used method for numerical solution of ordinary differential equations. Based on the obtained program, we simulated two populations and traced their behavior over time. We optimized the parameters and managed to obtain results that are very close to real data for such populations.

Prey Selection, Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System

2007 ◽  
Vol 69 (6) ◽  
pp. 1827-1846 ◽  
Author(s):  
Helen J. Edwards ◽  
Calvin Dytham ◽  
Jonathan W. Pitchford ◽  
David Righton
Keyword(s):  
Population Dynamics ◽  
Prey Selection ◽  
Predator Prey ◽  
Prey System

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.

scholarly journals The Asymptotic Behavior of a Stochastic Predator-Prey System with Holling II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhenwen Liu ◽  
Ningzhong Shi ◽  
Daqing Jiang ◽  
Chunyan Ji
Keyword(s):  
Population Dynamics ◽  
Asymptotic Behavior ◽  
Positive Solution ◽  
Functional Response ◽  
Dynamics Model ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Prey System ◽  
Population Dynamics Model ◽  
Holling Ii Functional Response

We discuss a stochastic predator-prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.

Data Processing for Dynamic Consequences of Prey Refuge in a Predator-Prey System with Stage Structure and Time Delay

2014 ◽  
Vol 978 ◽  
pp. 88-93
Author(s):  
Li Han
Keyword(s):  
Population Dynamics ◽  
Time Delay ◽  
Stage Structure ◽  
Equilibrium Density ◽  
Prey Refuge ◽  
Predator Prey ◽  
Data Process ◽  
Prey System ◽  
Stabilizing Effect ◽  
System With Time Delay

—In this paper, the effect of prey refuge on the dynamic consequences of the stage-structured predator-prey system with time delay are studied. The results indicate that the prey refuge play an important role in population dynamics, the extinction and coexistence of predator and prey population. The results show that the equilibrium density of immature and mature prey populations increase with increasing in prey refuge and the prey refuge has a clearly stabilizing effect on the predator-prey system with stage structure and time delay under a restricted set of conditions. The Data process is also analysized and obtained.

scholarly journals Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 72
Author(s):  
Anuraag Bukkuri ◽  
Joel S. Brown
Keyword(s):  
Game Theory ◽  
Drug Resistance ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Function Model ◽  
Predator Prey ◽  
Evolutionary Stable Strategies ◽  
Over Time

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

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