Ratio-dependent predator-prey model: effect of environmental fluctuation and stability

被引：181
作者：
Bandyopadhyay, M [1 ]
Chattopadhyay, J
机构：
[1] Indian Stat Inst, Embryol Res Unit, Kolkata 700108, W Bengal, India
[2] Scottish Church Coll, Dept Math, Kolkata 700006, W Bengal, India
来源：
NONLINEARITY | 2005年 / 18卷 / 02期
关键词：
D O I：
10.1088/0951-7715/18/2/022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the problem of a ratio-dependent predator-prey model. The deterministic and stochastic behaviour of the model system around biologically feasible equilibria are studied. Conditions for which the deterministic model enter into Hopf-bifurcation are worked out. Stochastic stability of the system around positive interior equilibrium is studied. To substantiate our analytical findings numerical simulations are carried out for a hypothetical set of parameter values.
引用
收藏
页码：913 / 936
页数：24
相关论文
共 63 条
[1]   Invulnerable prey and the paradox of enrichment [J].
Abrams, PA ;
Walters, CJ .
ECOLOGY, 1996, 77 (04) :1125-1133
[2]  
Afanas~ev V.N., 1996, MATH THEORY CONTROL
[3]   POPULATION-CYCLES OF MAMMALS - EVIDENCE FOR A RATIO-DEPENDENT PREDATION HYPOTHESIS [J].
AKCAKAYA, HR .
ECOLOGICAL MONOGRAPHS, 1992, 62 (01) :119-142
[4]   VARIATION IN PLANKTON DENSITIES AMONG LAKES - A CASE FOR RATIO-DEPENDENT PREDATION MODELS [J].
ARDITI, R ;
GINZBURG, LR ;
AKCAKAYA, HR .
AMERICAN NATURALIST, 1991, 138 (05) :1287-1296
[5]   THE BIOLOGICAL-CONTROL PARADOX [J].
ARDITI, R ;
BERRYMAN, AA .
TRENDS IN ECOLOGY & EVOLUTION, 1991, 6 (01) :32-32
[6]   COUPLING IN PREDATOR PREY DYNAMICS - RATIO-DEPENDENCE [J].
ARDITI, R ;
GINZBURG, LR .
JOURNAL OF THEORETICAL BIOLOGY, 1989, 139 (03) :311-326
[7]   Infection in prey population may act as a biological control in ratio-dependent predator-prey models [J].
Arino, O ;
El abdllaoui, A ;
Mikram, J ;
Chattopadhyay, J .
NONLINEARITY, 2004, 17 (03) :1101-1116
[8]  
BAISHYA MC, 1987, B MATH BIOL, V49, P125, DOI 10.1007/BF02459962
[9]   Dynamics of an autotroph-herbivore ecosystem with nutrient recycling [J].
Bandyopadhyay, M ;
Bhattacharyya, R ;
Mukhopadhyay, B .
ECOLOGICAL MODELLING, 2004, 176 (1-2) :201-209
[10]   Deterministic and stochastic analysis of a nonlinear prey-predator system [J].
Bandyopadhyay, M ;
Chakrabarti, CG .
JOURNAL OF BIOLOGICAL SYSTEMS, 2003, 11 (02) :161-172
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