Spring 2027

Applied Dynamical Systems, Chaos and Modeling

Introduction to nonlinear dynamical systems covering stability, bifurcations, and chaos, with an emphasis on applications from various scientific fields.

no offering record for this termCredits unavailable
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 7

Past student reviews · Matthew Johnston

Homework took forever and destroyed weekends. Exams were fairly difficult due to time pressure, though usually nothing came from out of left field.

What you’ll be able to do

  • 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.).

  • 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.).

  • 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.).

  • 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.).

  • 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.).

  • Design a mathematical model that embodies specific features of a physical or biological system (e.g., finite carrying capacity, predation).

  • Express informal mathematical arguments in English using appropriate mathematical terminology and notation.

Source: UW Guide

Grade history

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average GPA
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All recorded terms · compare terms & instructors

Prerequisites

Course map

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)

MATH 415 used by

“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

AMIR ASSADI is recorded teaching in Fall 2006. Recorded history may be incomplete and does not establish a future schedule.

JEAN-LUC THIFFEAULT is recorded teaching in Fall 2008, Fall 2015, Fall 2016, Fall 2017, Fall 2018, Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

MATTHEW JOHNSTON is recorded teaching in Fall 2012, Fall 2014. Recorded history may be incomplete and does not establish a future schedule.

POURIA BEHNOUDFAR is recorded teaching in Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

THIERRY LAURENS is recorded teaching in Fall 2024. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections.

Meeting source records
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Student experience

the class

Past student reviews · Thierry Laurens

Thierry Laurens managed to make ODEs fun with clear explanations. The first two-thirds of the course were very doable, while the final third was more conceptually challenging.

Recent recorded grades — Fall 2023: 3.06 GPA, 45.2% A/AB (n=31 letter grades); Fall 2024: 3.23 GPA, 60.0% A/AB (n=40 letter grades); Fall 2025: 3.47 GPA, 65.7% A/AB (n=35 letter grades).

difficulty & workload

Past student reviews · Matthew Johnston

Homework took forever and destroyed weekends. Exams were fairly difficult due to time pressure, though usually nothing came from out of left field.

Past student reviews · Pouria Behnoudfar

Pouria Behnoudfar’s midterm exam was described as insanely hard, but he graded it super leniently, giving points based on comprehension rather than accuracy.

Topics

  • Nonlinear dynamical systems, stability, bifurcations, and chaos
  • Applications in scientific fields

Skills

  • Identifying types of bifurcations in dynamical systems
  • Computing eigenvectors and drawing phase plane portraits
  • Designing mathematical models for physical or biological systems
  • Verifying stability properties of mathematical objects

Grades

Latest available · Fall 2025— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
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Grades over time

Through Fall 2025

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Fall 2025 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1316 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records

No offering records for the selected term.

Raw records 
[]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
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Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
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  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "0d86446db709b9efa150e0c534a9deec915e3c5e9863e720a662901b4eb110f4",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}