EAS 601 - Special Topics in Engineering Mathematics-Nonlinear Dynamics and Chaos

Institution:

University of Pennsylvania

Subject:

Description:

Prerequisite(s): Permission of Instructor. Continuous Dynamical Systems: Nonlinear Equations versus Linear Equations, One-Dimensional Flows: Flows on a Line, Fixed Points and Stability, Linear Stability Analysis, Potentials, Bifurcations, and Flows on the Circle. Two- Dimensional Flows: Linear Systems, Eigenvalues and Eigenvectors, Classification of Fixed Points, Phase Portraits, Conservative Systems, Reversible Systems, Index Theory, Limit Cycles, Gradient Systems, Liaponov Functions, Poincare-Bendixson Theorem, Lienard Systems, Relaxation Oscillations, Weakly Nonlinear Oscillators, Perturbation Theory, Saddle-Node, Transcritical and Pitchfork Bifurcations, Hopf Bifurcations, Global Bifurcations of Cycles, Hysteresis, and Poincare Maps. Three-Dimensional Flows: The Lorenz Equations, Strange Attractors and Chaos, The Lorenz Map. Discrete Dynamical Systems: One-Dimensional Maps, Chaos, Fixed Points and Cobwebs, The Liapunov Exponent, Universality and Feigenbaum's Number, Renormalization Theory, Fractals, Countable and Uncountable Sets, The Cantor Middle-Thirds Set, Self-Similar Fractals and Their Dimensions, The von Koch Curve, Box Dimension and Multifractals.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.upenn.edu

Phone Number:

(215) 898-5000

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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