Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay

[1]  Yuzhen Bai,et al.  New results on stability and boundedness of third order nonlinear delay differential equations , 2013 .

[2]  Yuliya N. Kyrychko,et al.  Stability and Bifurcations in an Epidemic Model with Varying Immunity Period , 2012, Bulletin of mathematical biology.

[3]  Wendi Wang,et al.  Global Stability for Two-Species Lotka)Volterra Systems with Delay* , 1997 .

[4]  S. Ruan DELAY DIFFERENTIAL EQUATIONS IN SINGLE SPECIES DYNAMICS , 2006 .

[5]  Daoyi Xu,et al.  Existence theorems for periodic Markov process and stochasticfunctional differential equations , 2009 .

[6]  Ryszard Rudnicki,et al.  Long-time behaviour of a stochastic prey–predator model , 2003 .

[7]  Yasuhisa Saito,et al.  The Necessary and Sufficient Condition for Global Stability of a Lotka–Volterra Cooperative or Competition System with Delays , 2002 .

[8]  Shengqiang Liu,et al.  Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching , 2017, 1707.06380.

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

[10]  Meng Liu,et al.  Stability in distribution of a three-species stochastic cascade predator-prey system with time delays , 2017 .

[11]  S. A. Campbell,et al.  Approximating the Stability Region for a Differential Equation with a Distributed Delay , 2009 .

[12]  Daqing Jiang,et al.  Long-time behaviour of a perturbed SIR model by white noise , 2013 .

[13]  Tonghua Zhang,et al.  Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects , 2017 .

[14]  Daqing Jiang,et al.  Stationary distribution and periodic solution for stochastic predator-prey systems with nonlinear predator harvesting , 2016, Commun. Nonlinear Sci. Numer. Simul..

[15]  D. Jiang,et al.  Periodic solutions for a stochastic non-autonomous Holling–Tanner predator–prey system with impulses , 2016 .

[16]  Wenjie Zuo,et al.  Stability and bifurcation analysis of a reaction–diffusion equation with spatio-temporal delay , 2015 .

[17]  Meng Liu,et al.  Stability of a budworm growth model with random perturbations , 2018, Appl. Math. Lett..

[18]  Teresa Faria,et al.  Global dynamics for Lotka-Volterra systems with infinite delay and patch structure , 2014, Appl. Math. Comput..

[19]  R. K. Miller On Volterra’s Population Equation , 1966 .

[20]  Ryszard Rudnicki,et al.  Influence of stochastic perturbation on prey-predator systems. , 2007, Mathematical biosciences.

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

[22]  Xue-Zhi Li,et al.  The Criteria for Globally Stable Equilibrium in n-Dimensional Lotka–Volterra Systems , 1999 .

[23]  Yongli Song,et al.  Stability and Hopf bifurcation in an unidirectional ring of n neurons with distributed delays , 2013, Neurocomputing.

[24]  Guodong Liu,et al.  Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps , 2017, Complex..

[25]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[26]  Wenjie Zuo,et al.  Stability and bifurcation analysis of a reaction–diffusion equation with distributed delay , 2015 .

[27]  Meng Liu,et al.  Dynamics of a stochastic regime-switching predator–prey model with harvesting and distributed delays , 2018 .

[28]  D. Jiang,et al.  Threshold Behavior in a Stochastic SIS Epidemic Model with Standard Incidence , 2014 .

[29]  Yanyan Han,et al.  Stability and Hopf bifurcation in a model of gene expression with distributed time delays , 2014, Appl. Math. Comput..

[30]  Xinzhu Meng,et al.  Optimal harvesting control and dynamics of two-species stochastic model with delays , 2017 .

[31]  Hopf bifurcations in a predator–prey system with a discrete delay and a distributed delay , 2010 .

[32]  R. Khasminskii Stochastic Stability of Differential Equations , 1980 .

[33]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[34]  B. Goh,et al.  Global stability in two species interactions , 1976, Journal of mathematical biology.