Mathematics for Dynamic Modeling
This new edition of Mathematics for Dynamic Modeling updates a widely used and highly-respected textbook. The text is appropriate for upper-level 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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Simple Dynamic Models
Ordinary Differential Equations
Stability of Dynamic Models
There is a Better
A Summary of Part 1
A reactiondiffusion model for morphogenesis A uniform
Cycles and Bifurcation
Bifurcation and Catastrophe
Including a model of algae bloom as a function of nutrient
References and a Guide to Further Readings
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 mass-spring mass—spring system mathematical motion moves negative nonlinear equations nullcline obtain occurs optimal orbit that begins oscillator parameters partial differential equations pendulum per-capita 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