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.

Optimizing the model of population dynamics in the “predator—prey” system

2004 ◽  
Vol 399 (1-6) ◽  
pp. 365-367
Author(s):  
T. R. Iskhakov ◽  
V. G. Soukhovolsky
Keyword(s):  
Population Dynamics ◽  
Predator Prey ◽  
Prey System

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.

Global attractivity of the predator–prey system for cotton aphid and seven-spot ladybird beetle with stage structure

2018 ◽  
Vol 11 (01) ◽  
pp. 1850012
Author(s):  
Lifei Zheng ◽  
Guixin Hu ◽  
Huiyan Zhao ◽  
M. K. D. K. Piyaratne ◽  
Aying Wan
Keyword(s):  
Population Dynamics ◽  
Numerical Simulations ◽  
Natural Enemies ◽  
Global Attractivity ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Cotton Aphid ◽  
Ladybird Beetle ◽  
Predator Prey ◽  
Prey System

It is well known that the cotton aphid is the major pest in cotton fields of Northwest China, and seven-spot ladybird is an important natural enemy among the various possible natural enemies of cotton aphid. In order to increase the applications of population dynamics in integrated pest management and control the cotton aphids biologically, we need to understand the population dynamics of cotton aphid and their natural enemies. A delay predator–prey system on cotton aphid and seven-spot ladybird beetle are proposed in this paper. Based on the comparison theorem and an iterative method, we investigate the global attractivity of the equilibrium points which have important biological meanings. Furthermore, some numerical simulations were carried out to illustrate and expand our theoretical results, in which a conjecture to generalize the well-known Theorem 16.4 in H. R. Thiemes book was put forward, which was taken as the open problem. The numerical simulations show coexistence of periodic solution, confirming the theoretical prediction.

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