Publication Cover
Applicable Analysis
An International Journal
Volume 29, 1988 - Issue 3-4
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Original Articles

Nonuniqueness of limit cycles of gause-type predator-prey systems

Pages 269-287 | Received 26 Feb 1988, Published online: 02 May 2007

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Yang Kuang. (1989) Finiteness of limit cycles in planar autonomous systems. Applicable Analysis 32:3-4, pages 253-264.
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Torsten Lindström. 2021. Handbook of the Mathematics of the Arts and Sciences. Handbook of the Mathematics of the Arts and Sciences 2275 2290 .
M Krishnadas, P P Saratchandran & K P Harikrishnan. (2020) Chaos in a cyclic three-species predator–prey system with a partial consumption of superpredator. Pramana 94:1.
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Alix M.C. Sauve, Rachel A. Taylor & Frédéric Barraquand. (2020) The effect of seasonal strength and abruptness on predator–prey dynamics. Journal of Theoretical Biology 491, pages 110175.
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Yanfei Dai, Yulin Zhao & Bo Sang. (2019) Four limit cycles in a predator–prey system of Leslie type with generalized Holling type III functional response. Nonlinear Analysis: Real World Applications 50, pages 218-239.
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Ting-Hao Hsu. (2019) Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death Rates. SIAM Journal on Applied Dynamical Systems 18:1, pages 33-67.
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Torsten Lindström. 2019. Handbook of the Mathematics of the Arts and Sciences. Handbook of the Mathematics of the Arts and Sciences 1 16 .
Hua Nie, Jianhua Wu & Wen-bin Yang. (2015) Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate. Communications on Pure and Applied Analysis 14:3, pages 1183-1204.
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Eduardo González‐Olivares & Alejandro Rojas‐Palma. (2012) Limit cycles in a Gause‐type predator–prey model with sigmoid functional response and weak Allee effect on prey. Mathematical Methods in the Applied Sciences 35:8, pages 963-975.
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Partha Sarathi Mandal & Malay Banerjee. (2012) Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model. Physica A: Statistical Mechanics and its Applications 391:4, pages 1216-1233.
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Sang-Hee Lee. (2011) Effects of the probability of a predator catching prey on predator–prey system stability. Journal of Asia-Pacific Entomology 14:2, pages 159-162.
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Eduardo González-Olivares & Alejandro Rojas-Palma. (2010) Multiple Limit Cycles in a Gause Type Predator–Prey Model with Holling Type III Functional Response and Allee Effect on Prey. Bulletin of Mathematical Biology 73:6, pages 1378-1397.
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Nurul Huda Gazi & Kalyan Das. (2010) Structural stability analysis of an algal bloom mathematical model in tropic interaction. Nonlinear Analysis: Real World Applications 11:4, pages 2191-2206.
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Karel Hasík. (2009) On a predator–prey system of Gause type. Journal of Mathematical Biology 60:1, pages 59-74.
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Dongmei Xiao & Zhifen Zhang. (2008) On the existence and uniqueness of limit cycles for generalized Liénard systems. Journal of Mathematical Analysis and Applications 343:1, pages 299-309.
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Dibakar Ghosh & A. Roy Chowdhury. (2007) On the Bifurcation Pattern and Normal Form in a Modified Predator–Prey Nonlinear System. Journal of Computational and Nonlinear Dynamics 2:3, pages 267-273.
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Jitsuro Sugie & Kyoko Kimoto. (2006) Homoclinic orbits in predator-prey systems with a nonsmooth prey growth rate. Quarterly of Applied Mathematics 64:3, pages 447-461.
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Dongmei Xiao & Huaiping Zhu. (2006) Multiple Focus and Hopf Bifurcations in a Predator-Prey System with Nonmonotonic Functional Response. SIAM Journal on Applied Mathematics 66:3, pages 802-819.
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Tapan Kumar Kar. (2005) Stability analysis of a prey–predator model incorporating a prey refuge. Communications in Nonlinear Science and Numerical Simulation 10:6, pages 681-691.
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Tapan Saha & Malay Bandyopadhyay. (2005) Dynamical analysis of a plant-herbivore model bifurcation and global stability. Journal of Applied Mathematics and Computing 19:1-2, pages 327-344.
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Debasis Mukherjee. (2003) Persistence and bifurcation analysis on a predator–prey system of holling type. ESAIM: Mathematical Modelling and Numerical Analysis 37:2, pages 339-344.
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Hai-bo Chen & Yi-rong Liu. (2001) Limit cycles in a generalized Gause-type predator-prey system. Journal of Central South University of Technology 8:4, pages 283-286.
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Edoardo Beretta & Yang Kuang. (1998) Global analyses in some delayed ratio-dependent predator-prey systems. Nonlinear Analysis: Theory, Methods & Applications 32:3, pages 381-408.
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R.E. Kooij & A. Zegeling. (1997) Qualitative properties of two-dimensional predator-prey systems. Nonlinear Analysis: Theory, Methods & Applications 29:6, pages 693-715.
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Mats Gyllenberg, Ilkka Hanski & Torsten Lindström. (1996) A predator-prey model with optimal suppression of reproduction in the prey. Mathematical Biosciences 134:2, pages 119-152.
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Torsten Lindstr�m. (1993) Qualitative analysis of a predator-prey system with limit cycles. Journal of Mathematical Biology 31:6, pages 541-561.
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. 1993. Delay Differential Equations - With Applications in Population Dynamics. Delay Differential Equations - With Applications in Population Dynamics 353 373 .
H.I. Freedman & Y. Kuang. (1990) Uniqueness of limit cycles in liénard-type equations. Nonlinear Analysis: Theory, Methods & Applications 15:4, pages 333-338.
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Yang Kuang. (1989) Limit Cycles in a Chemostat-Related Model. SIAM Journal on Applied Mathematics 49:6, pages 1759-1767.
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Yang Kuang. (1989) On the location and period of limit cycles in Gause-type predator-prey systems. Journal of Mathematical Analysis and Applications 142:1, pages 130-143.
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