We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the...We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.展开更多
In this paper,a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment.The model incorporates both white...In this paper,a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment.The model incorporates both white noise and telegraph noise,the latter being described by Markov process.The existence of a unique global positive solution for the stochastic chemostat model is established.Subsequently,by using the ergodic theory of Markov process and utilizing techniques of stochastic analysis,the critical value differentiating between persistence in mean and extinction for the microorganism species is explored.Moreover,the existence of a unique stationary distribution is proved by using stochastic Lyapunov analysis.Finally,numerical simulations are introduced to support the obtained results.展开更多
基金The NSF (10171010) of China Major Project of Education Ministry (01061) of China.
文摘We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.
基金supported by the Natural Science Foundation of Jiangsu Province,P.R.China(No.BK20220553)the China Postdoctoral Science Foundation(No.2023M742955)Z.Qiu's work was supported by the National Natural Science Foundation of China(No.12071217).
文摘In this paper,a stochastic framework with a general nonmonotonic response function is formulated to investigate the competition dynamics between two species in a chemostat environment.The model incorporates both white noise and telegraph noise,the latter being described by Markov process.The existence of a unique global positive solution for the stochastic chemostat model is established.Subsequently,by using the ergodic theory of Markov process and utilizing techniques of stochastic analysis,the critical value differentiating between persistence in mean and extinction for the microorganism species is explored.Moreover,the existence of a unique stationary distribution is proved by using stochastic Lyapunov analysis.Finally,numerical simulations are introduced to support the obtained results.
