In this paper,we consider two chemostat models w th random perturbation,in which single species depends on two perfectly substitutable resources for growth.For the autonomous system,we first prove that the solution of...In this paper,we consider two chemostat models w th random perturbation,in which single species depends on two perfectly substitutable resources for growth.For the autonomous system,we first prove that the solution of the system is positive and global.Then we establish sufficient conditions for the existence of an ergodic stationary distribu tion by constructing appropriate Lyapunov functions-For the non-autonomous system,by using Mas'minskii theory on periodic Markov processes,we derive it admits a nontriv ial positive periodic solution.Finally,numerical simulations are carried out to illustrate our main results.展开更多
Herein,we first report one-step synthesis of uniform Mo2 C microflowers(MCMFs)from low-cost precursors via industrialized solid-state strategy.With fine optimization in precursor ratio and pyrolysis temperatures,the a...Herein,we first report one-step synthesis of uniform Mo2 C microflowers(MCMFs)from low-cost precursors via industrialized solid-state strategy.With fine optimization in precursor ratio and pyrolysis temperatures,the as-fabricated MCMFs are assembled well with interconnected single-crystalline nanosheet subunits.More encouragingly,the resultant MCMFs are further highlighted as a competitive anode with robust and long-duration lithium-storage behaviors towards high-performance Li-ion batteries.展开更多
In this paper,we study the dynamical behavior of a stochastic two-compartment model of B-cell chronic lymphocytic leukemia,which is perturbed by white noise.Firstly,by constructing suitable Lyapunov functions,we estab...In this paper,we study the dynamical behavior of a stochastic two-compartment model of B-cell chronic lymphocytic leukemia,which is perturbed by white noise.Firstly,by constructing suitable Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary distribution.Then,conditions for extinction of the disease are derived.Furthermore,numerical simulations are presented for supporting the theoretical results.Our results show that large noise intensity may contribute to extinction of the disease.展开更多
基金the National Natural Science Foundation of P.R.China(No.11871473).
文摘In this paper,we consider two chemostat models w th random perturbation,in which single species depends on two perfectly substitutable resources for growth.For the autonomous system,we first prove that the solution of the system is positive and global.Then we establish sufficient conditions for the existence of an ergodic stationary distribu tion by constructing appropriate Lyapunov functions-For the non-autonomous system,by using Mas'minskii theory on periodic Markov processes,we derive it admits a nontriv ial positive periodic solution.Finally,numerical simulations are carried out to illustrate our main results.
基金financial support from National Natural Science Foundation of China(Nos.51772127,51772131,51802119)Taishan Scholars(No.ts201712050)Major Program of Shandong Province Natural Science Foundation(No.ZR2018ZB0317)。
文摘Herein,we first report one-step synthesis of uniform Mo2 C microflowers(MCMFs)from low-cost precursors via industrialized solid-state strategy.With fine optimization in precursor ratio and pyrolysis temperatures,the as-fabricated MCMFs are assembled well with interconnected single-crystalline nanosheet subunits.More encouragingly,the resultant MCMFs are further highlighted as a competitive anode with robust and long-duration lithium-storage behaviors towards high-performance Li-ion batteries.
基金This work is supported by the National Natural Science Foundation of China(No.11871473)Natural Science Foundation of Shandong Province(No.ZR2019MA010)Science and Technology Research Project of Jilin Provincial Department of Education of China(No.JJKH20180462KJ).
文摘In this paper,we study the dynamical behavior of a stochastic two-compartment model of B-cell chronic lymphocytic leukemia,which is perturbed by white noise.Firstly,by constructing suitable Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary distribution.Then,conditions for extinction of the disease are derived.Furthermore,numerical simulations are presented for supporting the theoretical results.Our results show that large noise intensity may contribute to extinction of the disease.
