scholarly journals Local Stability Analysis On Lotka-Volterra Predator-Prey Models Functional Responses With Constant prey Refuge

2021 ◽  
Author(s):  
Chongming Li
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Local Stability ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Stable Node ◽  
Type I ◽  
Type Ii ◽  
Functional Responses ◽  
Type Ii Functional Response

The dynamical behaviours of the predators and prey can be described by studying the local stability of the planar systems. Type I functional response shows that the rate of consumption per predator is proportional to prey’s density while type II functional response is related to the situation that predators would reach satiation as they consumed sufficient amount of prey. We seek out a method of using transformation to reduce the number of parameters of original models and then study the stability analysis of equilibrium points. Under suitable restrictions on the new parameters, we prove that the positive interior equilibrium is a stable node for the system of type I and type II functional responses. Moreover, in the case of type II functional response, the boundary equilibria can have more types of stability other than saddle points.

scholarly journals Local Stability Analysis On Lotka-Volterra Predator-Prey Models Functional Responses With Constant prey Refuge

2021 ◽  
Author(s):  
Chongming Li
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Local Stability ◽  
Equilibrium Points ◽  
Saddle Points ◽  
Stable Node ◽  
Type I ◽  
Type Ii ◽  
Functional Responses ◽  
Type Ii Functional Response

The dynamical behaviours of the predators and prey can be described by studying the local stability of the planar systems. Type I functional response shows that the rate of consumption per predator is proportional to prey’s density while type II functional response is related to the situation that predators would reach satiation as they consumed sufficient amount of prey. We seek out a method of using transformation to reduce the number of parameters of original models and then study the stability analysis of equilibrium points. Under suitable restrictions on the new parameters, we prove that the positive interior equilibrium is a stable node for the system of type I and type II functional responses. Moreover, in the case of type II functional response, the boundary equilibria can have more types of stability other than saddle points.

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.

Impact of fear on delayed three species food-web model with Holling type-II functional response

2021 ◽  
Author(s):  
S. Magudeeswaran ◽  
S. Vinoth ◽  
K. Sathiyanathan ◽  
M. Sivabalan
Keyword(s):  
Hopf Bifurcation ◽  
Food Web ◽  
Functional Response ◽  
Local Stability ◽  
Type Ii ◽  
Normal Form Theory ◽  
The Third ◽  
Delayed System ◽  
Food Web Model ◽  
Type Ii Functional Response

This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely [Formula: see text] and [Formula: see text], and the third species [Formula: see text] behaves as the predator and also host for [Formula: see text]. The species [Formula: see text] predating on the species [Formula: see text] with the Holling type-II functional response, while the first species [Formula: see text] is benefited from the third species [Formula: see text]. Further, the effect of fear is incorporated in the growth rate of species [Formula: see text] due to the predator [Formula: see text] and time lag in [Formula: see text] due to the gestation process. We explore all the biologically possible equilibrium points, and their local stability is analyzed based on the sample parameters. Next, we investigate the occurrence of Hopf-bifurcation around the interior equilibrium point by taking the value of the fear parameter as a bifurcation parameter for the non-delayed system. Moreover, we verify the local stability and existence of Hopf-bifurcation for the corresponding delayed system. Also, the direction and stability of the bifurcating periodic solutions are determined using the normal form theory and the center manifold theorem. Finally, we perform extensive numerical simulations to support the evidence of our analytical findings.

scholarly journals Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator

2020 ◽  
Vol 17 (2) ◽  
pp. 155-165
Author(s):  
A. Muh. Amil Siddik ◽  
Syamsuddin Toaha ◽  
Andi Muhammad Anwar
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Functional Response ◽  
Local Stability ◽  
Jacobian Matrix ◽  
Equilibrium Points ◽  
Type Iv ◽  
Simulation Results ◽  
Predator Model ◽  
Parameter Values

Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.  

scholarly journals Holling Type I versus Holling Type II functional responses in Gram-negative bacteria

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
O A Nev ◽  
H A van den Berg
Keyword(s):  
Functional Response ◽  
Cell Envelope ◽  
Building Blocks ◽  
Type I ◽  
Gram Negative Bacteria ◽  
Type Ii ◽  
Dynamic Adjustment ◽  
Functional Responses ◽  
Gram Negative ◽  
Molecular Building Blocks

AbstractWe consider how the double-membrane structure of the cell envelope of Gram-negative bacteria affects its functional response, which is the mathematical relationship that expresses how the nutrient uptake flux depends on environmental conditions. We show that, under suitable conditions, the Holling Type I functional response is a plausible model, as opposed to the Holling Type II (rectangular hyperbolic, ‘Michaelis–Menten’) response that is the default model in much of the literature. We investigate both diffusion-limited and capacity-limited regimes. Furthermore, we reconcile our findings with the preponderance in the established literature of hyperbolic models for the growth response, which are generally assumed to be valid, for both Gram-negative and Gram-positive bacteria. Finally, we consider the phenomenon of dynamic adjustment of investment of molecular building blocks in cellular components, and show how this will affect the functional response as observed by the experimenter.

scholarly journals Mutualisim between Two Species and a Mortal Predator with Holling Type-II Response Function

2019 ◽  
Vol 8 (2) ◽  
pp. 4070-4086
Keyword(s):  
Steady State ◽  
Global Stability ◽  
General Model ◽  
Local Stability ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Mutualistic Interaction ◽  
Boundary Equilibrium ◽  
Type Ii Functional Response

We analyze the dynamics of a general model of three-species mutualistic interaction among two species and a mortal predator, which consumes the first mutual species in terms of Holling type-II functional response manner. Local stability around the existing equilibrium points is investigated by using perturbed method. Sufficient conditions for the global stability are obtained by means of employing Lyapunov’s method around boundary equilibrium points. The population stochasticity around the steady state of co-existence due to white noise is also computed. Finally, the numerical illustrations are carried out to support the study

scholarly journals Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma
Keyword(s):  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Type Ii Functional Response

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

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