ROLE OF HARVESTING IN CONTROLLING CHAOTIC DYNAMICS IN THE PREDATOR–PREY MODEL WITH DISEASE IN THE PREDATOR

2013 ◽  
Vol 06 (02) ◽  
pp. 1350005 ◽  
Author(s):  
KRISHNA PADA DAS ◽  
SANJAY CHAUDHURI
Keyword(s):  
Chaotic Dynamics ◽  
Large Population ◽  
Model System ◽  
Predator Population ◽  
Predator Prey ◽  
Force Of Infection ◽  
Predator Prey Model ◽  
Prey Model ◽  
Reproduction Numbers

Predator–prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator–prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

Role of Alternative Food in Controlling Chaotic Dynamics in a Predator–Prey Model with Disease in the Predator

2016 ◽  
Vol 26 (09) ◽  
pp. 1650147 ◽  
Author(s):  
Krishna Pada Das ◽  
Nandadulal Bairagi ◽  
Prabir Sen
Keyword(s):  
Chaotic Dynamics ◽  
Period Doubling ◽  
Host Population ◽  
Alternative Food ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Oscillatory State ◽  
Prey Interaction

It is generally, but not always, accepted that alternative food plays a stabilizing role in predator–prey interaction. Parasites, on the other hand, have the ability to change both the qualitative and quantitative dynamics of its host population. In recent times, researchers are showing growing interest in formulating models that integrate both the ecological and epidemiological aspects. The present paper deals with the effect of alternative food on a predator–prey system with disease in the predator population. We show that the system, in the absence of alternative food, exhibits different dynamics viz. stable coexistence, limit cycle oscillations, period-doubling bifurcation and chaos when infection rate is gradually increased. However, when predator consumes alternative food coupled with its focal prey, the system returns to regular oscillatory state from chaotic state through period-halving bifurcations. Our study shows that alternative food may have larger impact on the community structure and may increase population persistence.

EFFECT OF PARASITIC INFECTION IN THE LESLIE–GOWER PREDATOR–PREY MODEL

2008 ◽  
Vol 16 (03) ◽  
pp. 425-444 ◽  
Author(s):  
MAINUL HAQUE ◽  
EZIO VENTURINO
Keyword(s):  
Biological Control ◽  
Control Parameter ◽  
Disease Incidence ◽  
Parasitic Infection ◽  
Logistic Growth ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

The Leslie–Gower predator–prey model with logistic growth in prey is here modified to include an SI parasitic infection affecting the prey population only. Thresholds are identified for the predator population to survive, and the conditions for the disease to die out naturally are given. The behavior of the system around each equilibrium is investigated, showing that the disease incidence may have a relevant influence on the dynamics of complex ecosytems, assuming at times the role of a biological control parameter.

scholarly journals A Mathematical Study of a Predator-Prey Dynamics with Disease in Predator

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Krishna pada Das
Keyword(s):  
Local Stability ◽  
Parasitic Infection ◽  
Model System ◽  
Predator Population ◽  
Mathematical Study ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Stability Analysis ◽  
Reproduction Numbers ◽  
Disease In Predator

We consider a predator-prey model where parasitic infection is spread in only predator population. We work out the local stability analysis of equilibrium point by the help of basic reproduction numbers. We also analyze the community structure of model system by the help of ecological as well as disease basic reproduction numbers. We derive Hopf bifurcation condition and permanence and impermanence of model system. We perform a numerical experiment and observe that parasitic infection in predator population stabilizes predator-prey oscillations.

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

Qualitative analysis of a diffusive Crowley–Martin predator–prey model: the role of nonlinear predator harvesting

2019 ◽  
Vol 98 (2) ◽  
pp. 1169-1189 ◽  
Author(s):  
Vandana Tiwari ◽  
Jai Prakash Tripathi ◽  
Syed Abbas ◽  
Jin-Shan Wang ◽  
Gui-Quan Sun ◽  
...  
Keyword(s):  
Qualitative Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Fear Induced Multistability in a Predator-Prey Model

2021 ◽  
Vol 31 (10) ◽  
pp. 2150150
Author(s):  
N. C. Pati ◽  
Shilpa Garai ◽  
Mainul Hossain ◽  
G. C. Layek ◽  
Nikhil Pal
Keyword(s):  
Parameter Space ◽  
Periodic Structures ◽  
Chaotic Oscillations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Prey Interaction ◽  
Type Ii Functional Response

In ecology, the predator’s impact goes beyond just killing the prey. In the present work, we explore the role of fear in the dynamics of a discrete-time predator-prey model where the predator-prey interaction obeys Holling type-II functional response. Owing to the increasing strength of fear, the system becomes stable from chaotic oscillations via inverse Neimark–Sacker bifurcation. Extensive numerical simulations are carried out to investigate the intricate dynamics for the organization of periodic structures in the bi-parameter space of the system. We observe fear induced multistability between different pairs of coexisting heterogeneous attractors due to the overlapping of multiple periodic domains in the bi-parameter space. The basin sets of the coexisting attractors are obtained and discussed at length. Multistability in the predator-prey system is important because the dynamics of the predator and prey populations in the critical parameter zone becomes uncertain.

THE ROLE OF ADDITIONAL FOOD IN A PREDATOR–PREY MODEL WITH A PREY REFUGE

2016 ◽  
Vol 24 (02n03) ◽  
pp. 345-365 ◽  
Author(s):  
SUDIP SAMANTA ◽  
RIKHIYA DHAR ◽  
IBRAHIM M. ELMOJTABA ◽  
JOYDEV CHATTOPADHYAY
Keyword(s):  
Stable Equilibrium ◽  
Predator Population ◽  
Stable Limit ◽  
Prey Refuge ◽  
Additional Food ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
The Impact

In this paper, we propose and analyze a predator–prey model with a prey refuge and additional food for predators. We study the impact of a prey refuge on the stability dynamics, when a constant proportion or a constant number of prey moves to the refuge area. The system dynamics are studied using both analytical and numerical techniques. We observe that the prey refuge can replace the predator–prey oscillations by a stable equilibrium if the refuge size crosses a threshold value. It is also observed that, if the refuge size is very high, then the extinction of the predator population is certain. Further, we observe that enhancement of additional food for predators prevents the extinction of the predator and also replaces the stable limit cycle with a stable equilibrium. Our results suggest that additional food for the predators enhances the stability and persistence of the system. Extensive numerical experiments are performed to illustrate our analytical findings.

Effects of prey refuges on a predator–prey model with a class of functional responses: The role of refuges

2009 ◽  
Vol 218 (2) ◽  
pp. 73-79 ◽  
Author(s):  
Zhihui Ma ◽  
Wenlong Li ◽  
Yu Zhao ◽  
Wenting Wang ◽  
Hui Zhang ◽  
...  
Keyword(s):  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Prey Refuges
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