Mathematics for Dynamic ModelingThis new edition of Mathematics for Dynamic Modeling updates a widely used and highlyrespected textbook. The text is appropriate for upperlevel undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, computer science, and economics. The text features many different realistic applications from a wide variety of disciplines. The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of interest.

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Contents
Simple Dynamic Models  3 
Ordinary Differential Equations  15 
Stability of Dynamic Models  29 
There is a Better  55 
A Summary of Part 1  71 
A reactiondiffusion model for morphogenesis A uniform  101 
Cycles and Bifurcation  121 
Bifurcation and Catastrophe  153 
Including a model of algae bloom as a function of nutrient  181 
References and a Guide to Further Readings  207 
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Common terms and phrases
A(Au algae assume asymptotically asymptotically stable attractor axis behavior budworm cars catastrophe model Chapter closed orbit Consider corresponding curve cusp catastrophe damping decreases defined denote density depends derivative differential equation dynamical systems eigenvalues Example Exercise follows frictional given gives growth Hopf bifurcation horizontal increases initial intersection interval Jacobian matrix jump Lemma Liapunov function limit cycle limit cycle exists linearized system mass massspring mass—spring system mathematical motion moves negative nonlinear equations nullcline obtain occurs optimal orbit that begins oscillator parameters partial differential equations pendulum percapita phase plane pitchfork bifurcation plankton pollutant population predator prey proportional rest point restoring force rocket roots rotates saddle point satisfies scalar Section shown in Figure shows slope smooth ſº spatial stable stable manifold Suppose surface Theorem traffic traveling wave solution unstable equilibrium variable vector field velocity vertical zero
Popular passages
Page 216  How Random is a Coin Toss?", Physics Today, April 1983, 18, and L. Kadanoff, "Roads to Chaos,