Institution: | aCollege of Science, Shandong University of Science and Technology, Qingdao 266510, PR China bDepartment of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China cSchool of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, PR China dInstitute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, PR China |
Abstract: | A nonautonomous Lotka–Volterra dispersal system with continuous delays and discrete delays is considered. By using a comparison theorem and delay differential equation basic theory, we obtain sufficient conditions for the permanence of the population in every patch. By constructing a suitable Lyapunov functional, we prove that the system is globally asymptotically stable under some appropriate conditions. Using almost periodic functional hull theory, we get sufficient conditions for the existence, uniqueness and globally asymptotical stability for an almost periodic solution. This implies that the population in every patch exhibits stable almost periodic fluctuation. Furthermore, the results show that the permanence and global stability of system, and the existence and uniqueness of a positive almost periodic solution, depend on the delay; then we call it “profitless”. |