Information Package / Course Catalogue
Nonlinear Dynamical Systems
Course Code: FİZ433
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 7
Objectives of the Course

Course Content

Name of Lecturer(s)
Learning Outcomes
1.To be able to obtain and classify the critical points of dynamic systems
2.To be able to analyze the stability of nonlinear dynamic systems using linearization and Liapunov functions
3.To be able to analyze the applications of applied mathematics or problems in different fields by using techniques of dynamic systems
4.Be able to identify and classify non-linear differential equations
5.To be able to determine approximate solutions of nonlinear differential equations using perturbation techniques.
Recommended or Required Reading
1.F. Verhulst, Non-linear Differential Equations and Dynamical Systems , Springer - Verlag, 1989.
2.Differential Equations, Dynamical Equations and Linear Algebra, M.W. Hirsch and S. Smale
3.Dynamical Systems with Applications using Mathematica. Stephen Lynch.
4.Invitation to Dynamical Systems. Edward R. Scheinerman
Weekly Detailed Course Contents
Week 1 - Theoretical
Linear theory of dynamic systems: Basic solutions, Autonomous linear systems and Phase portraits, critical points and stability
Week 2 - Theoretical
Nonlinear Dynamic systems: Autonomous nonlinear systems and Phase portraits, orbits and critical points
Week 3 - Theoretical
Linearization of nonlinear systems around critical point
Week 4 - Theoretical
Stability of linearization, asymptotic stability of solution, instability of periodic solutions
Week 5 - Theoretical
Periodic solutions, stability of periodic solutions, Hamiltonian systems and systems with first integrals
Week 6 - Theoretical
Conservative force fields and elliptical orbits, Hamiltonian mechanics, Volterra-Lotka hunting equations
Week 7 - Theoretical
Liapunov functions
Week 8 - Theoretical
Liapunov stability analysis
Week 9 - Intermediate Exam
Midterm Exam
Week 10 - Theoretical
ntroduction to irregularity theory, Poincare propagation theorem
Week 11 - Theoretical
Branching theory, central manifolds
Week 12 - Theoretical
Branching of critical points and Hopf branching
Week 13 - Theoretical
Chaos, Lorenz equations
Week 14 - Theoretical
One dimensional chaos
Week 15 - Theoretical
Lyapunov coefficients
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory1483154
Midterm Examination110212
Final Examination110313
TOTAL WORKLOAD (hours)179
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
4
4
OÇ-2
3
3
OÇ-3
3
4
OÇ-4
4
2
OÇ-5
3
Adnan Menderes University - Information Package / Course Catalogue
2026