title: Delay-induced periodic phenomenon in a diffusive regulated logistic model.
abstract: The diffusive logistic growth model with time delay and feedback control is considered. First, the well-posedness and permanence of solutions are discussed by using some comparison techniques. Then, the sufficient conditions for stability of nonnegative constant steady states are established, and the occurrence of Hopf bifurcation at positive steady state is performed. Next, the bifurcation properties are derived by computing the normal form on center manifold. Our results not only supplement but also generalized some existing ones. Finally, some numerical simulations show the feasibility of our theoretical analyses.
authors.affiliation: Business School, University of Shanghai for Science and Technology, Shanghai, 200093 China ; School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030 China.
authors.forename: Kejun
authors.initials: K
authors.lastname: Zhuang
authors.affiliation: College of Science, University of Shanghai for Science and Technology, Shanghai, 200093 China.
authors.forename: Gao
authors.initials: G
authors.lastname: Jia
keywords: Delay; Feedback control; Hopf bifurcation; Logistic model; Reaction–diffusion system