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Papers by Wei Feng
Journal of Mathematical Analysis and Applications, 1999
In this article we study the global stability in reaction-diffusion models for single-species pop... more In this article we study the global stability in reaction-diffusion models for single-species population growth under environmental toxicants with or without time delays. The existence and uniqueness of a positive steady-state solution are established in those models. It is shown that as long as the magnitude of the instantaneous self-limitation and toxicant effects is larger than that of the timedelay effects in the model with delays, the solution of both reaction-diffusion Ž systems has the same asymptotic behavior extinction or converging to the positive. steady-state solution, depending on the growth rate of the species. Numerical Ž. simulations for both cases with or without time delays are demonstrated for the purpose of comparison.
Journal of Mathematical Analysis and Applications, 1997
This paper studies a class of time-delay reaction᎐diffusion systems modeling the dynamics of sing... more This paper studies a class of time-delay reaction᎐diffusion systems modeling the dynamics of single or interacting populations. In the logistic equation, we prove that when the magnitude of the instantaneous term is larger than that of the delay terms, the population growth u has the same asymptotic limit as in the case of no delay. For the predator᎐prey model, a condition on the interaction rates is given to ensure the permanence effect in the ecosystem regardless of the length of delay intervals. A permanence condition is also obtained in the N-species competition system with time delays. It is shown that when the natural growth rate Ž. a , a,. .. , a is in an unbounded parameter set ⌳, the reaction᎐diffusion system 1 2 N has a positive global attractor. Finally, long-term behavior of the solutions for those time-delay systems is numerically demonstrated through finite-difference approximations and compared with the corresponding systems without delays.
In this paper, we study a new model obtained as an extension of a three-species food chain model ... more In this paper, we study a new model obtained as an extension of a three-species food chain model with ratio-dependent functional response. We provide non-persistence and permanence results and investigate the stability of all possible equilibria in relation to the ecological parameters. Results are obtained for the trivial and prey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studied using linearization. We provide a detailed analysis of conditions for existence, uniqueness, and multiplicity of coexistence equilibria, as well as permanent effect for all species. The complexity of the dynamics in this model is theoretically discussed and graphically demonstrated through various examples and numerical simulations.
Journal of Mathematical Analysis and Applications, 1999
In this article we study the global stability in reaction-diffusion models for single-species pop... more In this article we study the global stability in reaction-diffusion models for single-species population growth under environmental toxicants with or without time delays. The existence and uniqueness of a positive steady-state solution are established in those models. It is shown that as long as the magnitude of the instantaneous self-limitation and toxicant effects is larger than that of the timedelay effects in the model with delays, the solution of both reaction-diffusion Ž systems has the same asymptotic behavior extinction or converging to the positive. steady-state solution, depending on the growth rate of the species. Numerical Ž. simulations for both cases with or without time delays are demonstrated for the purpose of comparison.
Journal of Mathematical Analysis and Applications, 1997
This paper studies a class of time-delay reaction᎐diffusion systems modeling the dynamics of sing... more This paper studies a class of time-delay reaction᎐diffusion systems modeling the dynamics of single or interacting populations. In the logistic equation, we prove that when the magnitude of the instantaneous term is larger than that of the delay terms, the population growth u has the same asymptotic limit as in the case of no delay. For the predator᎐prey model, a condition on the interaction rates is given to ensure the permanence effect in the ecosystem regardless of the length of delay intervals. A permanence condition is also obtained in the N-species competition system with time delays. It is shown that when the natural growth rate Ž. a , a,. .. , a is in an unbounded parameter set ⌳, the reaction᎐diffusion system 1 2 N has a positive global attractor. Finally, long-term behavior of the solutions for those time-delay systems is numerically demonstrated through finite-difference approximations and compared with the corresponding systems without delays.
In this paper, we study a new model obtained as an extension of a three-species food chain model ... more In this paper, we study a new model obtained as an extension of a three-species food chain model with ratio-dependent functional response. We provide non-persistence and permanence results and investigate the stability of all possible equilibria in relation to the ecological parameters. Results are obtained for the trivial and prey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studied using linearization. We provide a detailed analysis of conditions for existence, uniqueness, and multiplicity of coexistence equilibria, as well as permanent effect for all species. The complexity of the dynamics in this model is theoretically discussed and graphically demonstrated through various examples and numerical simulations.