Stationary distribution and ergodicity of a stochastic hybrid competition model with Lévy jumps

[1]  Clark Jeffries,et al.  Stability of Predation Ecosystem Models , 1976 .

[2]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  R. Liptser.  A strong law of large numbers for local martingales , 1980 .

[4]  L. Rogers.  Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[5]  Joseph H. Connell,et al.  On the Prevalence and Relative Importance of Interspecific Competition: Evidence from Field Experiments , 1983, The American Naturalist.

[6]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[7]  J. Zabczyk,et al.  Ergodicity for Infinite Dimensional Systems: Invariant measures for stochastic evolution equations , 1996 .

[8]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[9]  Yong Xu,et al.  Stochastic Lotka--Volterra Population Dynamics with Infinite Delay , 2009, SIAM J. Appl. Math..

[10]  G. Yin,et al.  On competitive Lotka-Volterra model in random environments , 2009 .

[11]  Xuerong Mao,et al.  Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation , 2009 .

[12]  Xuerong Mao,et al.  Population dynamical behavior of Lotka-Volterra system under regime switching , 2009, J. Comput. Appl. Math..

[13]  A. Melnikov,et al.  On Comparison Theorem and its Applications to Finance , 2009 .

[14]  Michael Y. Li,et al.  Global-stability problem for coupled systems of differential equations on networks , 2010 .

[15]  H. Kunita.  Itô's stochastic calculus: Its surprising power for applications , 2010 .

[16]  Ke Wang,et al.  Stability in distribution of competitive Lotka–Volterra system with Markovian switching , 2011 .

[17]  Xuerong Mao,et al.  Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching , 2011 .

[18]  Xuerong Mao,et al.  Stationary distribution of stochastic population systems , 2011, Syst. Control. Lett..

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

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

[21]  Chenggui Yuan,et al.  Comparison Theorem for Stochastic Differential Delay Equations with Jumps , 2011, 1102.2165.

[22]  Miljana Jovanovic,et al.  Stochastic Gilpin-Ayala competition model with infinite delay , 2011, Appl. Math. Comput..

[23]  Daqing Jiang,et al.  Analysis of autonomous Lotka–Volterra competition systems with random perturbation , 2012 .

[24]  Daqing Jiang,et al.  Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System , 2013 .

[25]  Hong Liu,et al.  The ergodic property and positive recurrence of a multi-group Lotka-Volterra mutualistic system with regime switching , 2013, Syst. Control. Lett..

[26]  Qun Liu,et al.  Analysis on stochastic delay Lotka-Volterra systems driven by Lévy noise , 2014, Appl. Math. Comput..

[27]  Adel Settati,et al.  Stationary distribution of stochastic population systems under regime switching , 2014, Appl. Math. Comput..

[28]  Xiaoling Zou,et al.  Optimal harvesting for a stochastic regime-switching logistic diffusion system with jumps , 2014, Nonlinear Analysis: Hybrid Systems.

[29]  Guixin Hu.  Invariant distribution of stochastic Gompertz equation under regime switching , 2014, Math. Comput. Simul..

[30]  George Yin,et al.  Stochastic competitive Lotka-Volterra ecosystems under partial observation: Feedback controls for permanence and extinction , 2014, J. Frankl. Inst..

[31]  Meng Liu.  Global asymptotic stability of stochastic Lotka-Volterra systems with infinite delays , 2015 .

[32]  Zhijun Liu,et al.  On a nonautonomous competitive system subject to stochastic and impulsive perturbations , 2015, Appl. Math. Comput..

[33]  Xiaoling Zou,et al.  Optimal harvesting for a stochastic N-dimensional competitive Lotka-Volterra model with jumps , 2015 .

[34]  Qun Liu,et al.  The threshold of a stochastic Susceptible–Infective epidemic model under regime switching , 2016 .

[35]  Yu Zhao,et al.  Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps , 2016 .

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

[37]  Meng Liu,et al.  Permanence of Stochastic Lotka–Volterra Systems , 2017, J. Nonlinear Sci..

[38]  G. Yin,et al.  Switching diffusion logistic models involving singularly perturbed Markov chains: Weak convergence and stochastic permanence , 2017 .

[39]  George Yin,et al.  Coexistence and exclusion of stochastic competitive Lotka–Volterra models , 2016, 1601.06334.

[40]  D. O’Regan,et al.  Asymptotic behavior of a stochastic population model with Allee effect by Lévy jumps , 2017 .

[41]  Meng Liu,et al.  Persistence and extinction of a modified Leslie–Gower Holling-type II stochastic predator–prey model with impulsive toxicant input in polluted environments , 2018 .

[42]  Meng Liu,et al.  Dynamics of a stochastic delay competitive model with harvesting and Markovian switching , 2018, Appl. Math. Comput..