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Dynamics of competition. (English) Zbl 1002.92564
Capasso, V. (ed.) et al., Mathematics inspired by biology. Lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Martina Franca, Italy, June 13-20, 1997. Berlin: Springer. Lect. Notes Math. 1714, 191-240 (1999).
Contents: 1) Introduction; 2) Some Notation and Fundamental Results (Cones and Partial Orders, Basic Comparison Principle for ODEs, Comparison Principles for Parabolic PDEs); 3) Planar Competitive Systems (Periodically Forced Competitive Systems, Competitive Maps); 4) Phytoplankton Growth in Periodic Chemostat; 5) Autonomous Competitive Systems (General Results, 3-Dimensional Competitive Systems); 6) Examples of Competitive Systems in 3 (A Predator-Prey Model, Model of cAMP signaling in the Slime Mold, Model of a Mitotic Oscillator); 7) Abstract Dynamics of Competition; 8) Competition and Diffusion.
MSC:
92D40Ecology
34C60Qualitative investigation and simulation of models (ODE)
37N25Dynamical systems in biology
35Q80Appl. of PDE in areas other than physics (MSC2000)