250 research outputs found

    Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type

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    99學年度楊定揮教師升等代表著作 100學年度研究獎補助論文[[abstract]]In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c *, and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c *.[[incitationindex]]SCI[[booktype]]紙

    A stage-structured delayed reaction-diffusion model for competition between two species.

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    We formulate a delayed reaction-diffusion model that describes competition between two species in a stream. We divide each species into two compartments, individuals inhabiting on the benthos and individuals drifting in the stream. Time delays are incorporated to measure the time lengths from birth to maturity of the benthic populations. We assume that the growth of population takes place on the benthos and that dispersal occurs in the stream. Our system consists of two linear reaction-diffusion equations and two delayed ordinary differential equations. We study the dynamics of the non-spatial model, determine the existence and global stability of the equilibria, and provide conditions under which solutions converge to the equilibria. We show that the existence of traveling wave solutions can be established through compact integral operators. We define two real numbers and prove that they serve as the lower bounds of the speeds of traveling wave solutions in the system

    Permanence of a single-species dispersal system and predator survival

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    AbstractThis paper considers permanence of a single-species dispersal periodic system with the possibility of the loss for the species during their dispersion among patches. The condition obtained for permanence generalizes the known condition on the system without loss for the species in the process of movement. Next, we add predators into every patch and consider the survival possibility of the predator. It is shown that the total amount of the predators can remain positive, if the single-species (prey) dispersal system has a positive periodic solution and the quantity of prey in each patch is enough for survival of the predator

    Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

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    In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate the main results.Comment: 31page
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