Persistence and extinction of a modified Leslie–Gower Holling-type II stochastic predator–prey model with impulsive toxicant input in polluted environments

Abstract In this paper, a stochastic predator–prey model with modified Leslie–Gower Holling-type II schemes and impulsive toxicant input in polluted environments is developed and analyzed. The threshold between persistence in the mean and extinction is established for each population. Some simulation figures are also introduced to illustrate the theoretical results.

[1]  Jianjun Jiao,et al.  A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin , 2009 .

[2]  Xinyu Song,et al.  Dynamic behaviors of the periodic predator–prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect , 2008 .

[3]  Meng Liu,et al.  Analysis of a stochastic two-predators one-prey system with modified Leslie-Gower and Holling-type II schemes , 2017 .

[4]  M. A. Aziz-Alaoui,et al.  Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes , 2003, Appl. Math. Lett..

[5]  Bing Liu,et al.  The Effects of Impulsive Toxicant Input on a Population in a Polluted Environment , 2003 .

[6]  Meng Liu,et al.  Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle , 2010, Bulletin of mathematical biology.

[7]  Thomas G. Hallam,et al.  Effects of toxicants on populations: A qualitative: Approach III. Environmental and food chain pathways* , 1984 .

[8]  C. Braumann,et al.  Variable effort harvesting models in random environments: generalization to density-dependent noise intensities. , 2002, Mathematical biosciences.

[9]  Chuanzhi Bai,et al.  Population dynamical behavior of a two-predator one-prey stochastic model with time delay , 2017 .

[10]  M. Zhien,et al.  Thresholds of Survival for an n-Dimensional Volterra Mutualistic System in a Polluted Environment , 2000 .

[11]  X. Mao,et al.  Competitive Lotka–Volterra population dynamics with jumps , 2011, 1102.2163.

[12]  X. Mao,et al.  Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[13]  M. Zhien,et al.  The Thresholds of Survival for ann-Dimensional Food Chain Model in a Polluted Environment , 1997 .

[14]  J. Beddington,et al.  Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency , 1975 .

[15]  Daqing Jiang,et al.  Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation , 2009 .

[16]  Meng Liu,et al.  Optimal harvesting of a stochastic delay competitive model , 2017 .

[17]  Qun Liu,et al.  Dynamics of stochastic delay Lotka-Volterra systems with impulsive toxicant input and Lévy noise in polluted environments , 2015, Appl. Math. Comput..

[18]  Thomas G. Hallam,et al.  Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure , 1983 .

[19]  Chuanzhi Bai MULTIPLICITY OF SOLUTIONS FOR A CLASS OF NON-LOCAL ELLIPTIC OPERATORS SYSTEMS , 2017 .

[20]  E. Broughton The Bhopal disaster and its aftermath: a review , 2005, Environmental health : a global access science source.

[21]  T. Hallam,et al.  Effects of toxicants on populations: A qualitative approach II. first order kinetics , 1983, Journal of mathematical biology.

[22]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[23]  J. Gower,et al.  The properties of a stochastic model for the predator-prey type of interaction between two species , 1960 .

[24]  M. A. Aziz-Alaoui,et al.  Analysis of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with time delay , 2006 .

[25]  Ke Wang,et al.  Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps , 2013 .

[26]  Ke Wang,et al.  The survival analysis for a population in a polluted environment , 2009 .

[27]  Dejun Tan,et al.  Dynamics of a stochastic predator–prey system in a polluted environment with pulse toxicant input and impulsive perturbations , 2015 .

[28]  Meng Liu,et al.  Permanence and extinction in a stochastic service-resource mutualism model , 2017, Appl. Math. Lett..

[29]  R M May,et al.  Harvesting Natural Populations in a Randomly Fluctuating Environment , 1977, Science.

[30]  Zhen Jin,et al.  Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input☆ , 2007 .

[31]  P. H. Leslie SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS , 1948 .

[32]  Liu Huaping,et al.  The threshold of survival for system of two species in a polluted environment , 1991 .

[33]  G. Yin,et al.  On hybrid competitive Lotka–Volterra ecosystems , 2009 .

[34]  J. B. Shukla,et al.  Models for the effect of toxicant in single-species and predator-prey systems , 1991, Journal of mathematical biology.

[35]  Lei Zhang,et al.  Dynamics of a two-species Lotka-Volterra competition system in a polluted environment with pulse toxicant input , 2009, Appl. Math. Comput..

[36]  Qun Liu,et al.  Dynamical behaviors of a stochastic delay logistic system with impulsive toxicant input in a polluted environment. , 2013, Journal of theoretical biology.

[37]  Ke Wang,et al.  Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input , 2012 .

[38]  Daqing Jiang,et al.  A note on nonautonomous logistic equation with random perturbation , 2005 .

[39]  M. Keough,et al.  Field assessment of effects of timing and frequency of copper pulses on settlement of sessile marine invertebrates , 2000 .

[40]  Study of two-nutrient and two-micro-organism chemostat model with pulsed input in a polluted environment , 2015 .

[41]  J. F. Gilliam,et al.  FUNCTIONAL RESPONSES WITH PREDATOR INTERFERENCE: VIABLE ALTERNATIVES TO THE HOLLING TYPE II MODEL , 2001 .