APPLIED DYNAMICAL SYSTEMS, CHAOS AND MODELING

Prerequisites & course information

Requisites: MATH 341 , 376 , ( MATH 234 and 319 ), ( MATH 234 and 320 ), ( MATH 234 and 340 ), ( MATH 234 and 345 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions, properties, and theorems associated to linear and nonlinear dynamical systems (e.g., periodicity, critical points, chaotic behavior, contraction mapping principle, etc.). Audience: Undergraduate 2. Verify if a mathematical object has a given property used in elementary linear and nonlinear dynamical systems (e.g., if a set is stable, etc.). Audience: Undergraduate 3. Identify the type of bifurcation undergone by a dynamical system under a change of parameter values (e.g., saddle-node, pitchfork, and transcritical bifurcations, normal forms, etc.). Audience: Undergraduate 4. Check the premises of theorems used in elementary linear and nonlinear dynamical systems in order to apply their conclusions (e.g., that a function satisfies a particular inequality and hence must have a fixed point, etc.). Audience: Undergraduate 5. Resolve algebraic statements and perform standard computations and constructions related to elementary linear and nonlinear dynamical systems (e.g., computing eigenvectors, identifying invariant sets, draw a phase plane portrait, etc.). Audience: Undergraduate 6. Design a mathematical model that embodies specific features of a physical or biological system (e.g., finite carrying capacity, predation). Audience: Undergraduate 7. Express informal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate Learning Outcomes: 1. Recall and state the formal definitions, properties, and theorems associated to linear and nonlinear dynamical systems (e.g., periodicity, critical points, chaotic behavior, contraction mapping principle, etc.). Audience: Undergraduate 2. Verify if a mathematical object has a given property used in elementary linear and nonlinear dynamical systems (e.g., if a set is stable, etc.). Audience: Undergraduate 3. Identify the type of bifurcation undergone by a dynamical system under a change of parameter values (e.g., saddle-node, pitchfork, and transcritical bifurcations, normal forms, etc.). Audience: Undergraduate 4. Check the premises of theorems used in elementary linear and nonlinear dynamical systems in order to apply their conclusions (e.g., that a function satisfies a particular inequality and hence must have a fixed point, etc.). Audience: Undergraduate 5. Resolve algebraic statements and perform standard computations and constructions related to elementary linear and nonlinear dynamical systems (e.g., computing eigenvectors, identifying invariant sets, draw a phase plane portrait, etc.). Audience: Undergraduate 6. Design a mathematical model that embodies specific features of a physical or biological system (e.g., finite carrying capacity, predation). Audience: Undergraduate 7. Express informal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate