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 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 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 PREDATOR–PREY MODEL WITH AGE STRUCTURE

2017 ◽  
Vol 59 (2) ◽  
pp. 155-166
Author(s):  
J. PROMRAK ◽  
G. C. WAKE ◽  
C. RATTANAKUL
Keyword(s):  
Population Dynamics ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Green Lacewings ◽  
Cassava Plant ◽  
Age Dependent ◽  
Important Pest ◽  
Mckendrick Equation ◽  
Study Population ◽  
The Stability

Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated.

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 How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e2993 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C. Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body-mass dependent speed and capture success. We simulated these experiments in patches ranging from sizes of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fitted the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influenced stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig–MacArthur predator-prey model based on results from ourin silicoIBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in the smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

scholarly journals How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

2016 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

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 Singularity-Free Adaptive Controller for Uncertain Hysteresis Suspension Using Magnetorheological Elastomer-Based Absorber

2022 ◽  
Vol 2022 ◽  
pp. 1-17
Author(s):  
Hoa Thi Truong ◽  
Xuan Bao Nguyen ◽  
Cuong Mai Bui
Keyword(s):  
Parametric Uncertainty ◽  
Adaptive Controller ◽  
System Stability ◽  
Magnetorheological Elastomer ◽  
Unknown Parameters ◽  
Switching Algorithm ◽  
Neural Network Controller ◽  
Car Suspension ◽  
Network Controller ◽  
Smooth Switching

The magnetorheological elastomer (MRE) is a smart material widely used in recent vibration systems. A system using these materials often faces difficulties designing the controller such as unknown parameters, hysteresis state, and input constraints. First, a model is designed for the MRE-based absorber to portray the behavior of MRE and predict the appropriate electric current supplied. The conventional adaptive controller often suffers from so-called control singularities. The singularity-free adaptive controller is proposed to eliminate the singularity with parametric uncertainty. The proposed controller consists of four components: an adaptive linearizing controller, a deputy adaptive neural network controller, an auxiliary part designed for the controller to overcome the input constraint problem, and a smooth switching algorithm used to exchange the takeover rights of the two controllers. Moreover, the controller is designed to obtain the stabilization of hysteretic state estimation for the vibration system. The adaptive algorithms are proposed to update the unknown system parameters and to observe the unmeasurable hysteretic state. Meanwhile, closed-loop system stability is comprehensively assessed. Finally, the simulation performed on a quarter-car suspension with an MRE-based absorber shows the proposed controller's efficiency.

scholarly journals How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experiment

2016 ◽  
Author(s):  
Yuanheng Li ◽  
Ulrich Brose ◽  
Katrin Meyer ◽  
Björn C Rall
Keyword(s):  
Population Dynamics ◽  
Habitat Complexity ◽  
Patch Size ◽  
Feeding Rate ◽  
Interaction Strength ◽  
Time Frame ◽  
Feeding Rates ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model

Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.

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