scholarly journals Effects of Refuge Prey on Stability of the Prey-Predator Model Subject to Immigrants: A Mathematical Modelling Approach

2021 ◽  
Vol 47 (4) ◽  
pp. 1376-1391
Author(s):  
Mussa Amos Stephano ◽  
Il Hyo Jung
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Functional Response ◽  
Volterra Model ◽  
Predator Population ◽  
Type I ◽  
Proposed Model ◽  
Predator Model ◽  
Model Subject ◽  
Type Ii Functional Response

Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable and does not converge. However, with Holling’s type III functional response in a system, the proposed mathematical model is asymptotically stable. These results point out the following remarks: The effects of refuge prey on stability of the dynamical system vary depending on the type of functional response, and when the predator population increases, the likelihood of prey extinction declines when the proportion of preys in refuge population increases. Hence, the factor of refuge prey is crucial for controlling the population of the predator and obtaining balances between prey and predator in the ecosystem. Keywords: Refuge prey, stability, prey-predator, immigrants, Mathematical modelling

scholarly journals Stability of a fractional order harvested prey–predator model in the existence of infection in prey

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Subhashis Das ◽  
◽  
Sanat Mahato ◽  
Prasenjit Mahato
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Type I ◽  
Interior Equilibrium ◽  
Proposed Model ◽  
Different Types ◽  
Predator Model ◽  
Predictor Corrector ◽  
Uniqueness Criteria ◽  
Type Ii Functional Response

The growing relationship between prey and their predator is one of the important aspects in the field of ecology and mathematical biology. On the other hand, the utility of fractional calculus in different types of mathematical modelling have been applied extensively. In this paper, a fractional order prey–predator model is developed with the consideration of Holling type-I and Holling type-II functional response of the predator. As infection spreads through prey, the prey population is divided into two parts. In addition, we exploit the effect of harvesting to control the excessive spread of the infection. The existence and uniqueness criteria, the boundedness of the solution of the proposed model are investigated. A number of five possible equilibrium points of the proposed model are determined along with the feasibility conditions for each equilibrium points. The local stability at these equilibrium points and global stability at interior equilibrium point are investigated. Numerical simulation is presented with the help of modified Predictor-corrector method in MATLAB software to understand the dynamics of the proposed model.

scholarly journals Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Mikułowski ◽  
Rafał Wiszowaty
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Experimental Verification ◽  
Load Capacity ◽  
Mechanical Energy ◽  
Specific Situation ◽  
Engineering Structures ◽  
Piston Cylinder ◽  
Proposed Model ◽  
Energy Absorbers

Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

scholarly journals The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Raid Kamel Naji ◽  
Salam Jasim Majeed
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Dynamical Analysis ◽  
Local Bifurcation ◽  
Structure Population ◽  
Global Stability Analysis ◽  
Proposed Model ◽  
Predator Model ◽  
Predator System

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

scholarly journals Search Rate and Functional Response of a Eusocial Insect (Oecophylla longinoda) in a Tanzanian Mango Orchard

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Thora Samsø Fast ◽  
Jørgen Aagaard Axelsen ◽  
Gina Kier Lynegaard ◽  
Maulid Mwatawala ◽  
Joachim Offenberg
Keyword(s):  
Functional Response ◽  
Volterra Equation ◽  
Search Rate ◽  
Type I ◽  
Pest Species ◽  
Oecophylla Longinoda ◽  
Eusocial Insects ◽  
Volterra Models ◽  
Feeding Experiments ◽  
Type Ii Functional Response

Weaver ants,Oecophyllaspp., are famous for being efficient biological control agents as they prey on a variety of insects, and they are capable of suppressing a large number of pest species. Here, the search rate and functional response ofOecophylla longinodawere investigated in a Tanzanian mango orchard using feeding experiments. This was done by following the removal of prey, which constituted the foundation for estimating the search rate by aid of the Nicholson-Bailey and Lotka-Volterra models. The overall mean search rate was3.2 ×10-4and1.7 ×10-4over 30 minutes, when calculating the search rate using the Nicholson-Bailey equation and the Lotka-Volterra equation (modified Holling equation), respectively. The functional response investigations showed a linear relationship between removed prey and available prey, suggesting type I functional response or, alternatively, the initial phase of type II functional response. The results presented here are probably the first attempt to identify the functional response type of a colony of living predatory eusocial insects.

scholarly journals Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
James Huang
Keyword(s):  
Stability Analysis ◽  
Stage Structure ◽  
Model System ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Maturation Delay ◽  
Effort Level ◽  
Selective Harvest ◽  
Proposed Model ◽  
Predator Model

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

Functional response of kokanee salmon (Oncorhynchus nerka) to Daphnia at different light levels

2002 ◽  
Vol 59 (4) ◽  
pp. 707-716 ◽  
Author(s):  
Marci L Koski ◽  
Brett M Johnson
Keyword(s):  
Functional Response ◽  
Oncorhynchus Nerka ◽  
Search Time ◽  
Type I ◽  
Type Ii ◽  
Functional Responses ◽  
Foraging Mode ◽  
Kokanee Salmon ◽  
Light Levels ◽  
Type Ii Functional Response

In laboratory experiments, fingerling kokanee salmon (Oncorhynchus nerka, 3–8 g) were presented with varying densities of zooplankton prey (Daphnia spp.) ranging from 3 to 55 Daphnia·L–1, under three light intensities (30, 15, and 0.1 lx). Kokanee exhibited a type I functional response at 0.1 lx (Daphnia consumption·min–1 = 1.74 prey·L–1), a light level typical of moonlit epilimnetic conditions, but shifted to a type II functional response at higher light levels. Both 15 and 30 lx light levels occur during crepuscular periods when kokanee feeding is maximal in the wild, and consumption rates at these light levels were not significantly different (Daphnia consumption·min–1 = (163.6 prey·L–1)(42.2 prey·L–1)–1). The shift from the type I to type II functional response may be attributed to a foraging mode switch and the incorporation of search time instead of random encounters with prey. Using these models to simulate feeding rates in a Colorado reservoir, attenuation of light intensity and prey density between the epilimnion and hypolimnion resulted in a 100-fold increase in predicted feeding duration. Functional responses that incorporate environmental characteristics like light are important components of foraging models that seek to understand fish consumption, growth, and behavior.

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