scholarly journals Analysis of an Ecoepidemiological Model with Prey Refuges

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Shufan Wang ◽  
Zhihui Ma
Keyword(s):  
Functional Response ◽  
Contact Process ◽  
Global Perspective ◽  
Basic System ◽  
Stability Behavior ◽  
The Stability ◽  
Holling Iii Functional Response ◽  
Disease In Prey ◽  
Prey Refuges

An ecoepidemiological system with prey refuges and disease in prey is proposed. Bilinear incidence and Holling III functional response are used to model the contact process and the predation process, respectively. We will study the stability behavior of the basic system from a local to a global perspective. Permanence of the considered system is also investigated.

Dynamical Analysis of Prey Refuge in a Predator-Prey System with Rosenzweig Functional Response

2011 ◽  
Vol 271-273 ◽  
pp. 577-580
Author(s):  
Zhi Hui Ma ◽  
Shu Fan Wang ◽  
Wen Ting Wang
Keyword(s):  
Functional Response ◽  
Stability Property ◽  
Dynamical Analysis ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Stabilizing Effect ◽  
The Stability ◽  
Prey Refuges

In this paper, we proposed a predator-prey system incorporating Rosenzweig functional response and prey refuges. We will consider the stability property of the equilibria. Our results show that refuges using by prey have stabilizing effect on the considered system.

scholarly journals Stability Property for the Predator-Free Equilibrium Point of Predator-Prey Systems with a Class of Functional Response and Prey Refuges

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Fengde Chen ◽  
Yumin Wu ◽  
Zhaozhi Ma
Keyword(s):  
Equilibrium Point ◽  
Functional Response ◽  
Stability Property ◽  
Analytical Approach ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
The Stability ◽  
Prey Refuges

We investigate the stability property for the predator-free equilibrium point of predator-prey systems with a class of functional response and prey refuges by using the analytical approach. Under some very weakly assumption, we show that conditions that ensure the locally asymptotically stable of the predator-free equilibrium point are consistent with that of the globally asymptotically stable ones. Our result supplements the corresponding result of Ma et al., 2009.

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.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

scholarly journals The Effects of Media Coverage on the Dynamics of Disease in Prey-Predator Model

2021 ◽  
pp. 981-996
Author(s):  
Walaa Madhat Alwan ◽  
Huda Abdul Satar
Keyword(s):  
Media Coverage ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Proposed Model ◽  
Disease In Predator ◽  
Predator Model ◽  
The Stability ◽  
Effects Of Media ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effects is established and studied. An -type of disease in predator is considered.  All the properties of the solution of the proposed model are discussed. An application to the stability theory was carried out to investigate the local as well as global stability of the system. The persistence conditions of the model are determined. The occurrence of local bifurcation in the model is studied. Further investigation of the global dynamics of the model is achieved through using a numerical simulation.

scholarly journals Evaluation of the functional response of Chrysoperla carnea (Stephens) (Neuroptera:Chrysopidae) larvae feeding on cabbage aphid, Brevicoryne brassicae (L.)(Homoptera: Aphididae) in laboratory

2012 ◽  
Vol 9 (2) ◽  
pp. 220-228
Author(s):  
Baghdad Science Journal
Keyword(s):  
Functional Response ◽  
Attack Rate ◽  
Handling Time ◽  
Brevicoryne Brassicae ◽  
Chrysoperla Carnea ◽  
Nymphal Instar ◽  
Predator Satiation ◽  
Cabbage Aphid ◽  
The Stability ◽  
Type Ii Functional Response

This study evaluated the functional response of the larva of the predator Chrysoperla carnea by offering varying densities of cabbage aphid, Brevicoryne brassicae (L.) . Results showed conformity with type–II functional response, where the number of prey killed approaches asymptote hyperbolically as prey density increases (declining proportion of prey killed or the inverse density dependent) till it reached the stability stage determined by handling time and predator satiation. Also, the values of attack rate and handling time changed with age progress for both predator and prey. It has been observed an increase in the attack rate and reduction in handling time with the progress of the predator age when feeding on a particular nymphal instar. The attack rates of the predator was 1.779,3.406 and 4.219 ,while handling time was 0.015,0.010 and 0.008 (days) for 1st,2nd,3rd larval instars respectively, when fed on 1st nymphal instar. Also attack rates decreased and increases handling time with the progress in the prey. The attack rates were 1.779, 1.392, 1.096 and 1.059, due to an increase in size of the predator and in the growing efficiency in hunting the prey as well as in the increase in size of the prey and in developing its ability to defend itself and escape.

scholarly journals Abundant distinct types of solutions for the nervous biological fractional FitzHugh–Nagumo equation via three different sorts of schemes

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdel-Haleem Abdel-Aty ◽  
Mostafa M. A. Khater ◽  
Dumitru Baleanu ◽  
E. M. Khalil ◽  
Jamel Bouslimi ◽  
...  
Keyword(s):  
Nervous System ◽  
Expansion Method ◽  
B Spline ◽  
Stability Behavior ◽  
Nerve Impulses ◽  
Dynamical Behaviors ◽  
Different Types ◽  
Nagumo Equation ◽  
The Stability

Abstract The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model’s applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.

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