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Non Linear Systems
University of Galway - Direct Enroll Program
Galway, Ireland
Dates: 1/7/25 - 5/11/25
Non Linear Systems
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Other Subject Area: Physics
Instruction in: English
Course Code: MP491
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
This course is an introductuion to the analysis of systems of nonlinear Ordinary Differential Equations (ODEs) and Maps.
Learning Outcomes
1. Locate and calculate the stability for equilibria in 1-dim ODEs;
2. Locate and classify bifurcations for equilibria in 1-dim ODEs;
3. Locate, classify and calculate the stability for equilibria in linear 2-dim systems of ODEs;
4. Sketch phase-plane portraits about equilibria in linear 2-dim systems of ODEs;
5. Locate equilibria in nonlinear 2-dim systems of ODEs;
6. Linearise nonlinear 2-dim systems of ODEs, calculate the linear stability of equilibria and classify equilibria;
7. Sketch phase-plane portraits of nonlinear 2-dim systems of ODEs using iso-curves;
8. Analyse 2-dim Hamiltonian systems and sketch their phase-plane portraits;
9. Locate and classify Hopf bifurcations in nonlinear 2-dim systems of ODEs, and determine the stability of the corresponding limit cycles;
10. Locate and calculate the stability for fixed points and periodic orbits in 1-dim nonlinear maps;
11. Locate bifurcations in 1-dim nonlinear maps;
12. Describe period-doubling cascades to chaos in 1-dim nonlinear maps.
Learning Outcomes
1. Locate and calculate the stability for equilibria in 1-dim ODEs;
2. Locate and classify bifurcations for equilibria in 1-dim ODEs;
3. Locate, classify and calculate the stability for equilibria in linear 2-dim systems of ODEs;
4. Sketch phase-plane portraits about equilibria in linear 2-dim systems of ODEs;
5. Locate equilibria in nonlinear 2-dim systems of ODEs;
6. Linearise nonlinear 2-dim systems of ODEs, calculate the linear stability of equilibria and classify equilibria;
7. Sketch phase-plane portraits of nonlinear 2-dim systems of ODEs using iso-curves;
8. Analyse 2-dim Hamiltonian systems and sketch their phase-plane portraits;
9. Locate and classify Hopf bifurcations in nonlinear 2-dim systems of ODEs, and determine the stability of the corresponding limit cycles;
10. Locate and calculate the stability for fixed points and periodic orbits in 1-dim nonlinear maps;
11. Locate bifurcations in 1-dim nonlinear maps;
12. Describe period-doubling cascades to chaos in 1-dim nonlinear maps.