Mathematical Models in Biology
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
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analysis assumed assumptions axon bacterial behavior bifurcation Biol biological cell cellular changes Chapter characteristic equation chemical chemostat coefﬁcients complex concentration consider constant curve deﬁne deﬁnition density depends described determine difference equations differential equations diffusive instability dimensions discussed dynamics eigenvalues eigenvectors equa example ﬁeld ﬁgure ﬁnd ﬁrst ﬁxed ﬂow ﬂux function geometry glucose graph growth rate herbivores Hodgkin-Huxley model Hopf bifurcation theorem inﬁnite inﬂuence initial interactions Jacobian kinetics leads limit cycle linear Mathematical Models matrix membrane molecular molecules negative nonlinear nullcline nutrient obtain ordinary differential equations oscillations parameters parasitoid particles patterns perturbations phase-plane plane plant Poincaré-Bendixson theorem population positive predation predator-prey problem properties qualitative quantities reaction result saddle point satisﬁed Section Segel Show shown in Figure solution spatial species speciﬁc stable steady steady-state sufﬁciently system of equations theorem theory tion trajectory unstable values variables vector wavenumber York