Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Introduction to Discrete Dynamical System
Module Level: Bachelor
Abbreviation, if Applicable: MAM61306 Sub-Heading, if Applicable: -
Courses included in the module, if applicable
Introduction to Discrete Dynamical System
Semester/term: 5th / third years
Module Coordinator(s): Chair of the Lab. Applied Analysis and Numerical Computation Lectures(s) Prof. Dr. Agus Suryanto
Language Bahasa Indonesia
Classification within the curriculum
Elective Course
Teaching format / class hours per week during semester:
100 minutes lectures per week.
Workload: Total workload is 3 ECTS, which consists of 1.67 hours lectures, 2 hours structured activities, 2 hours independent learning, 16 week per semester, and a total 90.67 hours per semester including mid exam and final exam.
Credit Points: 2
Requirements according to the examination
regulations:
Students have attendance at least 80% on Introduction to Discrete Dynamical System class and registered as examinees in the academic information system
Recommended prerequisites
Students have taken Calculus III course (MAM61202), Difference Equations course (MAM61303) and have participated in the final examination of the course.
Learning
goals/competencies or
Module objectives/intended learning outcomes
After completing this course the student should have
CLO 1 : ability to understand discrete dynamical systems as mathematical models or the results of discretization of differential equations system
CLO 2 : ability to identify fixed point and periodic point of one- dimensional maps as well as to determine their stability CLO 3 : ability to understand elementary bifurcation in one-
dimensional maps
CLO 4 : ability to use software to simulate one-dimensional maps, including plotting Cobweb diagram, bifurcation diagram CLO 5 : ability to identify fixed point of two-dimensional linear and
nonlinear maps as well as to determine their stability
CLO 6 : ability to construct and interpret phase space diagram of two
Module Handbook-Mathematics-Universitas Brawijaya dimensional maps
CLO 7 : ability to use software to simulate two-dimensional maps CLO 8 : ability to do simple analysis on mathematical models which
are represented by discrete dynamical system (independently or in groups and responsibly), write the report and present it
Content: Topics:
1. Stability of one-dimensional maps: maps vs. differential equations, linear and nonlinear maps, fixed points, Cobweb diagram, Stability of hyperbolics and nonhyperbolics fixed points, periodic points and their stability, period-doubling route to chaos, basin of attraction, Singer’s theorem, bifurcations (saddle-node, trans-critical, pitchfork, period-doubling), Lyapunov exponent.
2. Stability of two-dimensional maps: linear maps, computing , fundamental set of solutions, phase-space diagrams, stability notion, stability of linear maps, stability via linearization.
3. Application of two-dimensional maps.
Attribut Soft Skill Discipline, honesty, cooperation and communication Study / exam
achevements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Assignment 25 %
2. Quiz 15 %
3. Mid examination 30 %
4. Paper (writing and presentation) 30 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media White/Black Board, LCD Projector, Laptop/Computer, Mathematical Software (e.g. Maple and MATLAB)
Learning Methods Lecture, Discussion, Presentation
Literature 1. Elaydi, S.N., 2007, Discrete Chaos with Applications in Science and Engineering, 2nd Edition, Chapman & Hall/CRC, Boca Raton.
2. Alligood, K. T., Sauer, T. D. and Yorke, J. A., 1996, Chaos - an Introduction to Dynamical Systems, Springer-Verlag New York, Inc.
Notes:
Module Handbook-Mathematics-Universitas Brawijaya
