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Dynamical Systems and their Applications in Biology

By: Shigui Ruan and Gail Wolkowicz

American Mathematical Society

Hardback | Feb 2003 | #139975 | ISBN: 0821831631
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About this book

Based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). Presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. Contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology.


A compartmental model of Cheyne-Stokes respiration; Integrated semigroup and linear ordinary differential equation with impulses; Interepidemic intervals in forced and unforced SEIR models; Stability analysis of time delayed chemostat models for bacteria and virulent phage; Hierarchical competition in discrete time models with dispersal; Stability and instability theorems for a characteristic equation arising in epidemic modeling; Some directions for mathematical epidemiology; Global attractivity of a population model with state-dependent delay; Metapopulation dynamics with migration and local competition; Oscillations and convergence in a harvesting model with sawtooth delay; Rigidity for differentiable classification of one-dimensional dynamical systems; Management of biological populations via impulsive control; Stability for a class of three-dimensional homogeneous systems; Change in criticality of synchronous Hopf bifurcation in a multiple-delayed neural system; Sharp conditions for global stability of Lotka-Volterra systems with delayed intraspecific competitions; Competition for essential resources: A brief review; 3/2 type criteria for global attractivity of Lotka-Volterra discrete system with delays; Epidemic solutions and endemic catastrophies; Persistence in almost periodic predator-prey reaction-diffusion systems

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