Course title
6M0004501
Nolinear Phenomena and Analysis

 IOKA Eri Click to show questionnaire result at 2018
Purpose of class
・To deepen understanding of physical phenomena observed in nonlinear systems, students will acquire numerical analysis skills through exercises using the Euler method, Runge–Kutta methods, and Newton’s method.
・From models described by equations of motion in classical physics, students will be able to obtain solution trajectories through numerical analysis for the cellular action potential model (Hodgkin–Huxley), which is represented by a system of nonlinear ordinary differential equations.
・Students will understand limit cycles observed in nonlinear systems and be able to perform simulations of them.
・Students will acquire fundamental knowledge and techniques for simulating models described by nonlinear ordinary differential equations.
Course content
In the environment surrounding us, there exist many nonlinear systems, such as airflow and traffic congestion, that cannot be described as linear phenomena. These systems exhibit dynamics and are modeled by equations; therefore, it is important to analyze how the behavior of their solutions changes with respect to parameters.
In this course, we focus on numerical analysis of ordinary differential equations as a method for simulating dynamical phenomena, and we analyze various models. Programming exercises will be conducted using Python.
Goals and objectives
  1. Students will be able to analyze explicit systems using the Euler method and Runge–Kutta methods.
    Students will be able to perform numerical computations using Newton’s method.
  2. Students will be able to explain the characteristics of limit cycles (closed trajectories).
    Students will be able to explain the stability of limit cycles in dynamical systems.
  3. Students will be able to numerically solve Hodgkin–Huxley-type neuron models (e.g., the FitzHugh–Nagumo model) using the fourth-order Runge–Kutta method.
    Students will be able to interpret results obtained through numerical simulations based on physiological knowledge.
  4. Students will be able to analyze the excitability of the FitzHugh–Nagumo model using phase diagrams and nullclines from a mathematical modeling perspective.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Total.
Total. -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Guidance 180minutes
2． Movement and differential equation 180minutes
3． Numerical calculation for ordinary differential equation 180minutes
4． Limit cycle oscillation 180minutes
5． Excitability cell and its mathematical models 177minutes
6． Stabilities and bifurcation of equilibrium points 180minutes
7． Stability analysis for equilibrium point in nonlinear system 180minutes
8． Exercises1 180minutes
9． Reporting on exercises1 180minutes
10． Exercises2 180minutes
11． Reporting on exercises2 180minutes
12． Exercises3 180minutes
13． Reporting on exercises3 180minutes
14． Summary of lecture 210minutes
Total. - 2547minutes
Evaluation method and criteria
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback outside of the class (ScombZ, mail, etc.)
Textbooks and reference materials
None
Prerequisites
None
Office hours and How to contact professors for questions
  • 水 12:40--13:20
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Fri Mar 20 04:05:46 JST 2026