Effects of intraspecific competition of prey in the dynamics of a food chain model
Tóm tắt
In this paper, dynamical behavior of simple prey-predator model with Holling type II functional response involving additional food for predator along with intraspecific competition of prey is proposed and analyzed. The stability criteria of solutions are investigated by varying quantity and quality of additional food and intraspecific competition of prey population. Conditions for Hopf bifurcation are derived analytically. Numerical simulation results are presented to observe the time evolution of the system. This study may be useful to understand the effects of intraspecific competition in real world ecological systems.
Tài liệu tham khảo
Agiza HN, Elabbasy EM, El Metwally H, Elsadany AA (2009) Chatoic dynamics of a discrete prey-predator model with Holling type II. Non Linear Anal Real World Appl 10:116–129
Manju Agarwal, Rachana Pathak (2012) Harvesting and hopf bifurcation in a prey-predator model with Holling type IV functional response. Int J Math soft comput 2(1):83–92
Akcakaya H, Arditi R, Ginzburg L (1995) Ratio-dependent predation: an abstraction that works. Ecology 76(3):995
Aziz-Alaoui M, Okiye MD (2003) Boundedness and global stability for a predator-prey model with modified LeslieGower and Holling-type II schemes. Appl Math Lett 16:1069–1075
Camara BI, Aziz - Alaoui MA, (2008) Complexity in a prey predator model. Int Conf Honor Claude Lobry 9:109–122
Chakraborty S, Tiwari PK, Misra AK, Chattopadhyay J (2015) Spatial dynamics of a nutrient phytoplankton system with toxic effect on phytoplankton. Math Biosci 264:94–100
Gakkhar S, Singh A (2012) Control of chaos due to additional predator in the Hastings Powell food chain model. J Math Anal Appl 385:423–438
Gibbsac M, Lacea LA, Jonesa MJ, Mooreb AJ (2004) Intraspecific competition in the speckled wood butterfly Pararge aegeria: effect of rearing density and gender on larval life history. J Insect Sci 4;(16):1-6. doi:10.1673/031.004.1601
Griffith DM, Poulson TL (1993) Mechanisms and consequences of intraspecific competition in a carabid cave beetle. Ecology 74(5):1373–1383
Holling CS (1959a) The components of predation as revealed by a study of Small mammal predation of the European pine sawfly. Can Entomol 91:293–320
Holling CS (1959b) Some characteristics of simple types of predation and Parasitism. Can Entomol 91:385–398
Holling CS (1965) The functional response of predators to prey density and its role in mimicry and population regulation. Mem Entomol Soc Can 45:5–60
Klomp H (1964) Intraspecific competition and the regulation of insect numbers. Ann Rev Entomol 9:17–40
Kumar R, Freedman HI (1989) A mathematical model of facultative mutualism with populations interaction in a food chain. Math Biosci 97:235–261
Lu Hongying, Wang Weigno (2011) Dynamics of a delayed discrete semi-ratio dependent predator-prey system with Holling type IV functional response. Adv Diff Equ :3-19
Mukherjee Debasis, Das Prasenjit and Kesh Dipak (2011) Dynamics of a plant - herbivore model with Holling type II functional response. Comput Math Biol. Issue :2(1)
Pal S, Chatterjee S, Das KP, Chattopadhyay J (2009) Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations. Ecol Model 220(2):96–110
Pitchford J, Brindley J (1998) Intratrophic predation in simple predator-prey models. Bull Math Biol 60:937–953
Prasad B, Banerjee M, Srinivasu PDN (2013) Dynamics of additional food provided predator prey system with mutually interfering predators. Math Biosci 246(1):176–190
Ross JV (2009) A note on density dependence in population models. Ecol Model 220:3472–3474
Ruan S, Xiao D (2001) Global analysis in a predator-prey system with non monotonic functional response. SIAM J Appl Math 61(4):1445–1472
Sahoo B, Poria S (2011) Dynamics of a predator-prey system with seasonal effects on additional food. Int J Ecosyst 1:10–13
Sahoo B, Poria S (2013) Disease control in a food chain model supplying alternative food. Appl Math Model 37(8):5653–5663
Sahoo B, Poria S (2013) Oscillatory coexistence of species in a food chain model with general Holling interactions. Differ Equ Dyn Syst. doi:10.1007/s12591-013-0171-9
Sahoo B, Poria S (2013) Disease control in a food chain model supplying alternative food. Appl Math Model 37:5653–5663
Sahoo B, Poria S (2014) Effects of supplying alternative food in a predator-prey model with harvesting. Appl Math Comput 234:150–166
Sahoo B, Poria S (2014) The chaos and control of a food chain model supplying additional food to top-predator. Chaos Solitons Fractals 58:52–64
Sahoo B, Poria S (2015) Effects of allochthonous inputs in the control of infectious disease of prey. Chaos Solitons Fractals 75:1–19
Saeez E, Gonzalez-Olivares E (1999) Dynamics of a predator-prey system. SIAM J Appl Math 59(5):1867–1878
Shanshan Chen, Junping Shi, Junjie Wei (2013) The effect of delay on a diffusive predator-prey system with Holling type-II predator functional response. Commun Pure Appl Anal 12(1):481–501
Skalski GT, Gilliam JF (2001) Functional responses with predator interference: viable alternatives to the Holling type II mode. Ecology 82:3083–3092
Sabelis MW, Rijn PC (2006) When does alternative food promote biological pest control? IOBC WPRS Bull 29:428–37
Sabelis MW, van Rijn PCJ (2005) When does alternative food promote biological pest control? In: Hoddle MS (ed) Proc. Second Int. Symp. Biol, Control of Arthropods, p 428–437
Srinivasu PDN, Prasad BSRV, Venkatesulu M (2007) Biological control through provision of additional food to predators : atheoretical study. Teor Popul Bio 1(72):111–120
Srinivasu PDN, Prasad BSRV (2010) Time optimal control of an additional food provided predator prey system with applications to pest management and biological conservation. J Math Biol 60:591–613
Srinivasu PDN, Prasad B (2011) Role of quantity of additional food to predators as a control in predator prey systems with relevance to pest management and biological conservation. Bull Math Biol 73(10):2249–2276
Wang W, Wang H, Li Z (2007) The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy. Chaos Solitons Fractals 32:1772–1785
Yujing Gao (2013) Dynamics of ratio-dependent predator prey system with a strong Allee effect. Discrete Contin Dyn Syst ser B 18(9):2283–2313
Zhang ZZ, Yang HZ, (2013) Hopf bifurcation in a delayed predator-prey system with modified Leslie-gower and Holling type III schemes. ACTA AUTOMATICA SINICA 39(5):610–616
Zhang Lei, Wang Weiming, Xue Yakui, Jin Zhen (2008) Complex dynamics of a Holling-type IV predator prey model. arXiv:0801.4365 [q-bio.PE]:1-23