Continuous Threshold Harvesting Intermediate Predator in Food Chain Model
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Abstract
This paper presents a three-species food chain system, which consists of intermediate predator population that depends only on prey population, and top predator population that depends only on intermediate predator population. We study this model when the intermediate predator exposed to the risk of harvest.
We studied the bounded solutions and equilibrium points with its conditions. Also the stability for each equilibrium points was studied. We determine the invariant region, in this region all population are survive and continuous harvesting. At last, we describe some results in numerical simulation
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References
[1] Bohn, Jonathan, J. S. K. Rebaza, (2011).
Continuous threshold prey harvesting in predatorprey
models, International Journal of Computational
and Mathematical Sciences 5(2): 111–118.
[2] Butler, G., Hsu, S. and Waltman, P. (1983).
Coexistence of competing predators in a chemostat,
Journal of mathematical biology 17(2): 133–151.
[3] Chauvet, E., Paullet, J. E., Previte, J. P. and
Walls, Z. (2002). A lotka-volterra three-species food
chain, Mathematics Magazine pp. 243–255.
[4] Dubey, B., Chandra, P. and Sinha, P. (2003). A
model for fishery resource with reserve area,
Nonlinear Analysis: Real World Applications 4(4):
625–637.
[5] Freedman, H. and Waltman, P. (1984).
Persistence in models of three interacting predatorprey
populations, Mathematical biosciences 68(2):
213–231.
[6] Gakkhar, S. and Naji, R. (2003). Seasonally
perturbed prey-predator system with predatordependent
functional response, Chaos, Solitons and
Fractals 18(5): 1075–1083.
[7] Haque, M. and Venturino, E. (2006). The role of
transmissible diseases in the holling-tanner predatorprey
model, Theoretical Population Biology 70(3):
273–288.
[8] Hesaaraki, M. and Moghadas, S.(2001). Existence
of limit cycles for predator-prey systems with a class
of functional responses, Ecological Modelling 142(1):
1–9.
[9] Hethcote, H. (2000). The mathematics of
infectious diseases, SIAM review 42(4): 599–653.
[10] Hwang, T. (2003). Global analysis of the
predator-prey system with beddington-deangelis
functional response, Journal of mathematical analysis
and applications 281(1): 395–401.
[11] Kumar Kar, T. (2006). Modelling and analysis of
a harvested prey-predator system incorporat-ing a
prey refuge, Journal of Computational and Applied
Mathematics 185(1): 19–33.
[12] Naji, R. and Balasim, A. (2007). Dynamical
behavior of a three species food chain model with
beddington-deangelis functional response, Chaos,
Solitons and Fractals 32(5): 1853–1866.
[13] Upadhyay, R. and Naji, R. (2009). Dynamics of
a three species food chain model with crowleymartin
type functional response, Chaos, Solitons and
Fractals 42(3): 1337–1346.
[14] Wuhaib, S. A and Abu Hassan, Y, (2013).
Continuous threshold prey harvesting with vulnerable
infected prey, AIP Conf. Proc. 1522, 561-575.
[15] Xiao, D., Li, W. and Han, M. (2006). Dynamics
in a ratio-dependent predator-prey model with
predator harvesting, Journal of mathematical analysis
and applications 324(1): 14–29.
[16] Xiao, Y. N. and Chen, L. S. (2004). Global
stability of a predator-prey system with stage
structure for the predator, Acta Mathematica Sinica
20(1): 63–70.