SI2540 Complex Systems 7.5 credits

Komplexa system

Complex systems, a.k.a. dynamical systems, refer to mathematical models describing the time evolution of systems by means of equations of motion and initial values. It is the solutions rather than the systems, or the models of the systems, that display complex features. Examples of such features are various ordered processes and structures, such as nonlinear oscillations and waves, as well as disordered chaotic processes and fractal structures. The models are formulated in terms of coupled nonlinear differential equations or, in the discrete case, as iterated maps. Nonlinearity is essential and key concepts are bifurcations, sensitive dependence on initial values, attractors and chaos. There are applications to physics, biology, chemistry, engineering and other areas. The course deals with analytical and numerical methods for the analysis of nonlinear models based on a small number of independent variables.

  • Education cycle

    Second cycle
  • Main field of study

  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Spring 19 for programme students

Spring 19 SAP for Study Abroad Programme (SAP)

  • Periods

    Spring 19 P4 (7.5 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus


  • Tutoring time


  • Form of study


  • Number of places *

    Max. 5

    *) If there are more applicants than number of places selection will be made.

  • Schedule

    Schedule (new window)

  • Course responsible

    Jack Lidmar <>

  • Teacher

    Ralf Eichhorn <>

  • Target group


  • Application

    Apply for this course at through this application link.
    Please note that you need to log in at to finalize your application.

Spring 20 for programme students

Intended learning outcomes

Upon completion of the course, you will 

  • be familiar with analytical and numerical methods for the analysis of coupled nonlinear differential equations
  • be able to interpret and characterize different solution types
  • know, and be able to develop, applications to physics, biology, chemistry, engineering and other areas

Course main content

Coupled nonlinear differential equations. Phase space, trajectories. Iterative maps. Stability analysis of singular points. Limit cycles, strange attractors. Poincaré-Bendixson theorem. Bifurcations. Chaos. Lyapunov exponents. Feigenbaum renormalization. Fractals, fractal dimensions. Lorenz equations, logistic map, Hénon map, Rössler system. Applications to Physics, Biology, Chemistry, Engineering: Lasers. Superconducting Josephson junctions. Population dynamics. Chemical kinetics. Electronic oscillators. Nonlinear mechanical systems.


Recommended prerequisites: Basic course in differential equations.


Steven H. Strogatz: Nonlinear Dynamics and Chaos (Westview Press, 2000, ISBN 0-7382-0453-6).


  • INL1 - Assigment, 7.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

Home assignments and an oral exam (INL1 + TEN1; 7,5 hp).

Offered by

SCI/Undergraduate Physics


Jack Lidmar (


Jack Lidmar <>

Supplementary information

Thecourse canbe canceled if there is less then 10 students


Course syllabus valid from: Autumn 2008.
Examination information valid from: Autumn 2007.