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Exactly solvable models of ...
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monografia Rebiun07942697 https://catalogo.rebiun.org/rebiun/record/Rebiun07942697 061016s2006 xxu u0|||||eng 2005048466 9781584885214 1584885211 UIB (230257) UPVA 990002638400203706 CBUC 991041429149706706 DLC. DLC. B-UPV 574 Petrovskii, Sergei V. Exactly solvable models of biological invasion Sergei V. Petrovskii, Bai-Lian Li Boca Raton [etc.] Chapman & Hall/CRC 2006 Boca Raton [etc.] Boca Raton [etc.] Chapman & Hall/CRC 217 p. il. 25 cm 217 p. Chapman & Hall/CRC mathematical biology and medicine series INTRODUCTIONWhy exactly solvable models are importantIntra- and inter-species interactions and local population dynamicsBasic mechanisms of species transportBiological invasion: main facts and constituting examplesMODELS OF BIOLOGICAL INVASIONDiffusion-reaction equationsIntegral-difference modelsSpace-discrete modelsStochastic modelsConcluding remarksBASIC METHODS AND RELEVANT EXAMPLESThe Cole-Hopf transformation and the Burgers equation as a paradigmFurther application of the Cole-Hopf transformationMethod of piecewise linear approximationExact solutions of a generalized Fisher equationMore about ansatzSINGLE-SPECIES MODELSImpact of advection and migrationAccelerating population wavesThe problem of critical aggregationDENSITY-DEPENDENT DIFFUSIONThe Aronson-Newman solution and its generalizationStratified diffusion and the Allee effectMODELS OF INTERACTING POPULATIONSExact solution for a diffusive predator-prey systemMigration waves in a resource-consumer systemSOME ALTERNATIVE AND COMPLEMENTARY APPROACHESWave speed and the eigenvalue problemConvergence of the initial conditionsConvergence and the paradox of linearizationApplication of the comparison principleECOLOGICAL EXAMPLES AND APPLICATIONSInvasion of Japanese beetle in the United StatesMount St. Helens recolonization and the impact of predationStratified diffusion and rapid plant invasionAPPENDIX: BASIC BACKGROUND MATHEMATICSOrdinary differential equations and their solutionsPhase plane and stability analysisDiffusion equationReferencesIndex Biología de poblaciones- Modelos matemáticos Biological invasions-Mathematical models Li, Bai-Lian