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

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 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.

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.

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.

scholarly journals Temperature alters the shape of predator–prey cycles through effects on underlying mechanisms

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9377 ◽  
Author(s):  
John P. DeLong ◽  
Shelby Lyon
Keyword(s):  
Population Dynamics ◽  
Model Parameters ◽  
Cycle Period ◽  
Short Term ◽  
Ecological Dynamics ◽  
Predator Prey ◽  
Prey System ◽  
Wide Range ◽  
Underlying Mechanisms ◽  
Temperature Dependance

Background Predicting the effects of climate warming on the dynamics of ecological systems requires understanding how temperature influences birth rates, death rates and the strength of species interactions. The temperature dependance of these processes—which are the underlying mechanisms of ecological dynamics—is often thought to be exponential or unimodal, generally supported by short-term experiments. However, ecological dynamics unfold over many generations. Our goal was to empirically document shifts in predator–prey cycles over the full range of temperatures that can possibly support a predator–prey system and then to uncover the effect of temperature on the underlying mechanisms driving those changes. Methods We measured the population dynamics of the Didinium-Paramecium predator–prey system across a wide range of temperatures to reveal systematic changes in the dynamics of the system. We then used ordinary differential equation fitting to estimate parameters of a model describing the dynamics, and used these estimates to assess the long-term temperature dependance of all the underlying mechanisms. Results We found that predator–prey cycles shrank in state space from colder to hotter temperatures and that both cycle period and amplitude varied with temperature. Model parameters showed mostly unimodal responses to temperature, with one parameter (predator mortality) increasing monotonically with temperature and one parameter (predator conversion efficiency) invariant with temperature. Our results indicate that temperature can have profound, systematic effects on ecological dynamics, and these can arise through diverse and simultaneous changes in multiple underlying mechanisms. Predicting the effects of temperature on ecological dynamics may require additional investigation into how the underlying drivers of population dynamics respond to temperature beyond a short-term, acute response.

scholarly journals Asexual reproduction changes predator population dynamics in a life predator–prey system

2019 ◽  
Vol 61 (2) ◽  
pp. 210-216 ◽  
Author(s):  
Thomas Scheuerl ◽  
Claus‐Peter Stelzer
Keyword(s):  
Population Dynamics ◽  
Asexual Reproduction ◽  
Predator Population ◽  
Predator Prey ◽  
Prey System
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