An official website of the United States government
Abstract A dynamic reaction–diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment.
more »
« less
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
-
The bistable dynamics of a modified Nicholson's blowflies delay differential equation with Allee effect is analyzed. The stability and basins of attraction of multiple equilibria are studied by using Lyapunov-LaSalle invariance principle. The existence of multiple periodic solutions are shown using local and global Hopf bifurcations near positive equilibria, and these solutions generate long transient oscillatory patterns and asymptotic stable oscillatory patterns.more » « less
-
It is shown that for any positive integer \begin{document}$$ n \ge 3 $$\end{document}, there is a stable irreducible \begin{document}$$ n\times n $$\end{document} matrix \begin{document}$ A $$\end{document} with \begin{document}$$ 2n+1-\lfloor\frac{n}{3}\rfloor $$\end{document} nonzero entries exhibiting Turing instability. Moreover, when \begin{document}$$ n = 3 $$\end{document}, the result is best possible, i.e., every \begin{document}$$ 3\times 3 $$\end{document} stable matrix with five or fewer nonzero entries will not exhibit Turing instability. Furthermore, we determine all possible \begin{document}$$ 3\times 3 $$\end{document} irreducible sign pattern matrices with 6 nonzero entries which can be realized by a matrix \begin{document}$$ A $$\end{document}$ that exhibits Turing instability.more » « less
-
Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.more » « less
