Chaos in a Lotka–Volterra predator–prey system with periodically impulsive ratio-harvesting the prey and time delays

[1]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[2]  R. Gaines,et al.  Coincidence Degree and Nonlinear Differential Equations , 1977 .

[3]  Jim M Cushing,et al.  Two species competition in a periodic environment , 1980 .

[4]  W M Schaffer,et al.  Can nonlinear dynamics elucidate mechanisms in ecology and epidemiology? , 1985, IMA journal of mathematics applied in medicine and biology.

[5]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[6]  S Pavlou,et al.  Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies. , 1992, Mathematical biosciences.

[7]  Mark Kot,et al.  Complex dynamics in a model microbial system , 1992 .

[8]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[9]  Yuri A. Kuznetsov,et al.  Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities , 1993 .

[10]  Alan Hastings,et al.  Chaos in three species food chains , 1994 .

[11]  J. Panetta,et al.  A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment. , 1996, Bulletin of mathematical biology.

[12]  Xinzhi Liu,et al.  Permanence of population growth models with impulsive effects , 1997 .

[13]  Lansun Chen,et al.  Density-dependent birth rate, birth pulses and their population dynamic consequences , 2002, Journal of mathematical biology.

[14]  S. Gakkhar,et al.  Order and chaos in predator to prey ratio-dependent food chain , 2003 .

[15]  Xianning Liu,et al.  Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator ☆ , 2003 .

[16]  Lansun Chen,et al.  The study of predator–prey system with defensive ability of prey and impulsive perturbations on the predator , 2005 .

[17]  Lansun Chen,et al.  Complexity of an SIR epidemic dynamics model with impulsive vaccination control , 2005 .

[18]  Fengyan Wang,et al.  Permanence and Complexity of a Three Species Food Chain with Impulsive Effect on the Top Predator , 2005 .

[19]  Fengyan Wang,et al.  Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat ☆ , 2006 .