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 Intraspecific variation stabilizes classic predator-prey dynamics

2021 ◽  
Author(s):  
Stefano Allesina ◽  
Zachary R Miller ◽  
Carlos Andres Marcelo Servan
Keyword(s):  
Intraspecific Variation ◽  
Self Regulation ◽  
Intraspecific Variability ◽  
Predator Prey ◽  
New Class ◽  
Predator Prey Model ◽  
Prey Model ◽  
Vito Volterra ◽  
Parameter Values ◽  
Consumer Resource

In 1920, Alfred J. Lotka found that, to his "considerable surprise", the dynamics of a simple predator-prey model he had devised led "to undamped, and hence indefinitely continued, oscillations"---which he thought epitomized the "rhythm of Nature" dear to the Victorians. In 1926, the same model was proposed independently by mathematician Vito Volterra, who was inspired by the work of his son-in-law, fish biologist Umberto D'Ancona. For over a century, the equations that now bear their names have served as a template for the development of sophisticated models for population dynamics. Coexistence in this classic predator-prey model is fragile---stochasticity or temporal variability in parameter values result in extinctions. The dynamics can be stabilized by intraspecific competition or other forms of self-regulation, but the prevalence of these processes in large food webs has been questioned. Here we show that when we consider populations characterized by intraspecific variability, dynamics are stable---despite the absence of any direct self-regulation. Our results can be generalized further, defining a new class of consumer-resource models. By accounting for intraspecific variation, which is manifest in all biological populations, we obtain dynamics that differ qualitatively and quantitatively from those found for homogeneous populations---challenging a central assumption of many ecological models.

scholarly journals Model matematis predator-prey tanaman padi, hama penggerek batang, tikus, dan wereng batang coklat di Karawang

2018 ◽  
Vol 13 (1) ◽  
pp. 52-62
Author(s):  
Tesa Nur Padilah ◽  
Betha Nurina Sari ◽  
Hannie Hannie
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Brown Planthopper ◽  
Stem Borer ◽  
Behavioral Analysis ◽  
Predator Prey ◽  
Rice Plants ◽  
Predator Prey Model ◽  
Prey Model ◽  
Plant Pest

Karawang merupakan salah satu pusat penanaman padi di Pulau Jawa. Keberhasilan panen dapat terganggu oleh adanya organisme pengganggu tumbuhan (OPT) sehingga dapat mengancam target swasembada beras. Hubungan antara tanaman padi dengan OPT dapat dibentuk menjadi suatu model matematis yaitu model predator-prey. Untuk itu, penelitian ini bertujuan untuk menganalisis model matematis predator-prey tanaman padi dan OPT. Predator (pemangsa) adalah makhluk hidup yang memakan mangsa (prey). Model predator-prey antara tanaman padi dengan OPT yang dibahas adalah model tiga predator yaitu hama penggerek batang, tikus, dan wereng batang coklat dengan prey yaitu padi. Pertumbuhan padi mengikuti model pertumbuhan logistik. Model yang diturunkan berbentuk sistem persamaan diferensial nonlinier. Pada model diperoleh lima titik ekuilibrium. Analisis perilaku model dilakukan pada tiga titik ekuilibrium dan ketiganya bersifat stabil asimtotik. Simulasi model dengan menggunakan software Maple 13 sejalan dengan analisis perilaku model. Faktor-faktor yang berpengaruh agar populasi hama penggerek batang, tikus, dan wereng batang coklat dapat menurun bahkan hilang dari populasi yaitu tingkat kematian alami serta tingkat interaksi padi terhadap hama-hama tersebut. Predator-prey mathematical model of rice plants, stem borer, rat, and brown planthopper in Karawang AbstractKarawang was one of the center of rice planting in Java Island. The success of the harvest may be disrupted by the presence of plant pest organisms that may threaten the rice self-sufficiency target. The relationship between rice plants and pests can be formed into a mathematical model, that was a predator-prey model. Therefore, this research aimed to analyze the mathematical model of predator-prey between rice plants and plant pest organisme. Predators were living things that eat prey. The predator-prey model between rice plants and pests discussed was a three predator model of stem borer, rat, and brown stem rhizome with the prey, that was rice. Rice growth follows the logistic growth model. The derived model was an nonlinear differential equation system. In this model obtained five equilibrium points. Model behavioral analysis was performed on three equilibrium points and they were stable asymptotically. Simulations of the model using Maple 13 software were in good agreement with behavioral analysis model. Factors that influence the stem borer, rat, and brown planthopper population could decrease even disapear from the population were the natural death rate and the interaction rate of rice to the pests.

A Markov-switching predator–prey model with Allee effect for preys

2020 ◽  
Vol 13 (03) ◽  
pp. 2050018
Author(s):  
Xiaoxia Guo ◽  
Zhiming Guo
Keyword(s):  
Numerical Simulations ◽  
Allee Effect ◽  
Global Attractivity ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results ◽  
Prey Populations

This paper concerns with a Markov-switching predator–prey model with Allee effect for preys. The conditions under which extinction of predator and prey populations occur have been established. Sufficient conditions are also given for persistence and global attractivity in mean. In addition, stability in the distribution of the system under consideration is derived under some assumptions. Finally, numerical simulations are carried out to illustrate theoretical results.

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 Immune dynamics in a time of covid

2021 ◽  
Author(s):  
Troy Shinbrot
Keyword(s):  
Mathematical Model ◽  
Immune System ◽  
Disease Progression ◽  
Adaptive Immunity ◽  
Recurrent Infections ◽  
Immunomodulatory Agents ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Mathematical Model

Motivated by curiosities of disease progression seen in the coronavirus pandemic, we analyze a minimalist predator-prey model for the immune system (predator) competing against a pathogen (prey). We find that the mathematical model alone accounts for numerous paradoxical behaviors observed in this and other infections. These include why an exponentially growing pathogen requires an exposure threshold to take hold, how chronic and recurrent infections can arise, and what can allow very sick patients to recover, while healthier patients succumb. We also examine the distinct dynamical roles that specific, innate, and nonspecific, adaptive, immunity play, and we describe mathematical effects of infection history on prognosis. Finally, we briefly discuss predictions for some of the effects of timing and strengths of antibiotics or immunomodulatory agents.

Sign in / Sign up

Export Citation Format

Share Document