Global dynamics of zooplankton and harmful algae in flowing habitats
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In this article, the authors study two advection-dispersion-reaction models arising from the dynamics of harmful algae and zooplankton in flowing-water habitats where a main channel is coupled to a hydraulic storage zone.About:
This article is published in Journal of Differential Equations.The article was published on 2013-08-01 and is currently open access. It has received 54 citations till now. The article focuses on the topics: Algae & Zooplankton.read more
Citations
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Dynamics and profiles of a diffusive host–pathogen system with distinct dispersal rates
Yixiang Wu,Xingfu Zou,Xingfu Zou +2 more
TL;DR: In this article, the authors investigated a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts and proved that the solution of the model exists globally and the model system possesses a global attractor.
Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith
TL;DR: Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.
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Influence of human behavior on cholera dynamics.
TL;DR: The results show that human behavior can reduce (a) the endemic and epidemic levels, (b) cholera spreading speeds and (c) the risk of infection (characterized by the basic reproduction number).
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Global dynamics of a PDE in-host viral model
TL;DR: In this article, an in-host virus dynamics model with spatial heterogeneity on the general bounded domain, and homogenous Neumann boundary condition, is considered, under the assumption that only the free virus diffuse and the host cells are not mobile.
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$R_0$ Analysis of a Benthic-Drift Model for a Stream Population
Qihua Huang,Yu Jin,Mark A. Lewis +2 more
TL;DR: A process-oriented benthic-drift model is developed that links changes in the flow regime and habitat availability with population dynamics and develops new theory to calculate these quantities and use them to investigate how the various flow regimes, population birth rate, individual transfer rates between zones, and river heterogeneity affect populati...
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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Semigroups of Linear Operators and Applications to Partial Differential Equations
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
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Nonlinear Functional Analysis
TL;DR: A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.
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Maximum principles in differential equations
TL;DR: The One-Dimensional Maximum Principle (MDP) as mentioned in this paper is a generalization of the one-dimensional maximum principle (OMP) for the construction of hyperbolic equations.