A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochas...A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.展开更多
The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)...The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].展开更多
基金supported by the National Natural Science Foundation of China(11271101)the NNSF of Shandong Province(ZR2010AQ021)
文摘A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.
基金This work is supported by the NNSF of China and the NSF of Hunan Province
文摘The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].
