Information Package / Course Catalogue
Nonlinear System Theory
Course Code: EEE504
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

To describe the dynamics of nonlinear systems encountered in science and engineering, to understand the nature of nonlinear systems, to explain how some nonlinear systems go into chaos, and to understand the characteristics of chaos.

Course Content

Nonlinear systems, system dynamics, phase space, bifurcation, stabiility, attractors, Lyapunov stability , ergodicity equation, logistic mapping, chaos.

Name of Lecturer(s)
Learning Outcomes
1.To be able to understand system dynamics and phase space
2.To be able to understand the bifurcation theory
3.To be able to determine stability of systems and to understand the Lyapunov stability
4.To understand the logistic equation and its mapping
5.To understand chaos and its conditions
Recommended or Required Reading
1.S. H. Strogatz, Nonlinear Dynamics and Chaos, Perseus Books 1994, Massachusetts
2.R. H. Rand, Lecture Notes on Nonlinear Vibrations ,Cornell University Press, NewYork, 2001Erwin Kreyszig, Advanced Engineering Mathematics Seventh Edition, Wiley (2006)
3. L. N. Virgin, Introduction to Experimental Nonlinear Dynamics, Cambridge University Press, 2000, Cambridge
Weekly Detailed Course Contents
Week 1 - Theoretical
Review of linear vibration systems, concepts of system dynamics, phase space and stability concepts
Week 2 - Theoretical
One dimensional nonlinear systems-I: stability
Week 3 - Theoretical
One dimensional nonlinear systems-II: bifurcations
Week 4 - Theoretical
One dimensional nonlinear systems-III: Flows on the circle (uniform and non-uniform oscillator, overdamped pendulum, Science & engineering applications)
Week 5 - Theoretical
Two dimensional nonlinear systems-I: Definitions, examples and classifications of linear systems
Week 6 - Theoretical
Two dimensional nonlinear systems-II: Phase plane (Phase portraits, existence and uniqueness, fixed points and linearization, conservative systems, reversible systems, pendulum, index theory, Science & engineering applications)
Week 7 - Theoretical
Two dimensional nonlinear systems-III: Limit cycles (Ruling out closed orbits, Lienard systems, relaxation oscillator, weakly nonlinear oscillations)
Week 8 - Theoretical
Review-Midterm Exam
Week 9 - Theoretical
Bifurcation revisited-I: Saddle-node, Trans-critical, and Pitchfork bifurcations, Hopf Bifurcations and cycles
Week 10 - Theoretical
Bifurcation revisited-II: Oscillating chemical reactions, Global bifurcations of cycles, hysteresis in the driven pendulum and Josephson junction, Coupled oscillators and quasi-periodicity, Poincare maps
Week 11 - Theoretical
Lorentz equations, chaos on a strange attractor, Lorenz map, using chaos to send secret messages
Week 12 - Theoretical
One dimensional maps-I: Fixed point and cobwebs, logistic map: Numerics
Week 13 - Theoretical
One dimensional maps-II: logistic map: analysis, periodic windows, Lyapunov exponent, universality and experiments, renormalization
Week 14 - Theoretical
Stability of nonlinear systems, Lyapunov stability, Review and Science & Engineering applications
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Quiz1%5
Midterm Examination1%20
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment110212
Quiz1628
Midterm Examination115318
Final Examination125328
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
OÇ-1
4
3
4
3
4
4
4
OÇ-2
3
3
3
4
3
3
4
OÇ-3
4
4
3
5
4
5
4
OÇ-4
4
4
4
3
4
3
4
OÇ-5
4
5
4
5
4
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026