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.

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.

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.

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.

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.

scholarly journals Predator–Prey Model Based Asymmetry Resource Allocation in Satellite–Terrestrial Network

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2113
Author(s):  
Zhipeng Li ◽  
Meng Li ◽  
Qian Wang
Keyword(s):  
Resource Allocation ◽  
Satellite Networks ◽  
Volterra Model ◽  
Network Resources ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model ◽  
Optimal Resource ◽  
Terrestrial Network

In the traditional satellite networks, network resources are mainly allocated among all the satellites based on the same allocation algorithm. This kind of symmetry model limits the increase of throughput. In this paper, we study an asymmetry resource allocation method in a satellite–terrestrial network and propose a Lotka–Volterra based predator–prey model to achieve optimal resource allocation among different satellites. In the proposed satellite–terrestrial network, we divide all the satellites into two groups, and we try to achieve load stability between these two satellites groups. Using the predator–prey model, one group is the prey–satellites, which can obtain service requirements from mobile users. The other group is considered as predator–satellites, which can only obtain the loads from the group of the prey–satellites. Once the satellites are divided into two groups using the Lotka–Volterra model, the resource allocation problem among these satellites in two groups would be asymmetry resource. We prove the existence of solutions to the proposed model. Numerical simulation results are given to show the correctness and effectiveness of the proposed model.

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.

scholarly journals The Control Data Method: A New Method of Modeling in Population Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lin-Fei Nie ◽  
Zhi-Dong Teng
Keyword(s):  
Population Dynamics ◽  
Approximation Property ◽  
Volterra Model ◽  
Unknown Parameters ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Neural Network Controller ◽  
Network Controller ◽  
Machine Learning Approach ◽  
Factual Data

A novel modeling method for population dynamics is developed. Based on the classical Lotka-Volterra model, we construct a new predator-prey model with unknown parameters to simulate the behaviors of predator and prey. Using a the approximation property and the machine learning approach of artificial neural networks, a tuning algorithm of unknown parameters is obtained and the factual data of predator-prey can be asymptotically stabilized using a neural network controller. Numerical examples and analysis of the results are presented.

scholarly journals Stochastic dynamics of predator-prey interactions

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255880
Author(s):  
Abhyudai Singh
Keyword(s):  
Attack Rate ◽  
Stochastic Dynamics ◽  
Volterra Model ◽  
Reproduction Rate ◽  
Predator Population ◽  
Population Densities ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Predator Attack

The interaction between a consumer (such as, a predator or a parasitoid) and a resource (such as, a prey or a host) forms an integral motif in ecological food webs, and has been modeled since the early 20th century starting from the seminal work of Lotka and Volterra. While the Lotka-Volterra predator-prey model predicts a neutrally stable equilibrium with oscillating population densities, a density-dependent predator attack rate is known to stabilize the equilibrium. Here, we consider a stochastic formulation of the Lotka-Volterra model where the prey’s reproduction rate is a random process, and the predator’s attack rate depends on both the prey and predator population densities. Analysis shows that increasing the sensitivity of the attack rate to the prey density attenuates the magnitude of stochastic fluctuations in the population densities. In contrast, these fluctuations vary non-monotonically with the sensitivity of the attack rate to the predator density with an optimal level of sensitivity minimizing the magnitude of fluctuations. Interestingly, our systematic study of the predator-prey correlations reveals distinct signatures depending on the form of the density-dependent attack rate. In summary, stochastic dynamics of nonlinear Lotka-Volterra models can be harnessed to infer density-dependent mechanisms regulating predator-prey interactions. Moreover, these mechanisms can have contrasting consequences on population density fluctuations, with predator-dependent attack rates amplifying stochasticity, while prey-dependent attack rates countering to buffer fluctuations.

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