2018 Nonlinear Dynamics

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Academic unit or major
Graduate major in Systems and Control Engineering
Nakao Hiroya 
Class Format
Media-enhanced courses
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Course description and aims

Various real-world phenomena are modeled as dynamical systems. In this course, starting with the elements of dynamical systems theory, destabilization of stationary states and emergence of spontaneous rhythmic or chaotic dynamics are explained, using mathematical models of real-world systems as examples.

Student learning outcomes

The aim of this course is to provide knowledge on the elements of dynamical systems theory such as stability and bifurcation, as well as on the dynamical systems modeling of real-world phenomena. In particular, theoretical and numerical analysis of nonlinear oscillations will be discussed.


Dynamical systems, stability, nonlinear oscillations, chaos, synchronization

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

lectures, homework

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction / Phase space and flows Understand the notion of phase space and flows
Class 2 One-dimensional dynamical systems Understand the dynamics of one-dimensional systems
Class 3 Two-dimensional dynamical systems Understand the dynamics on the two-dimensional phase plane
Class 4 Stability and bifurcation Understand the linear stability analysis and destabilization of fixed points
Class 5 Limit-cycle oscillations Understand the emergence of limit-cycle oscillations and typical examples
Class 6 Reduction methods Understand the methods to simplify dynamical systems
Class 7 Synchronization Understand the synchronization phenomena of nonlinear oscillations
Class 8 Chaos Understand the emergence of chaos and its characterization


Steven Strogatz, "Nonlinear dynamics and chaos", Westview press.

Reference books, course materials, etc.

Kuramoto, "Chemical Oscillations, Waves, and Turbulence", Springer.
Hoppensteadt & Izhikevich, "Weakly Connected Neural Networks", Springer.

Assessment criteria and methods

Grading will be based on the homework scores.

Related courses

  • SCE.A501 : Networks and Coupled Dynamical Systems
  • MTH.C341 : Differential Equations I
  • MTH.C342 : Differential Equations II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Elementary knowledge of mathematics and physics

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