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MA4H0 - Applied Dynamical Systems

  • Module code: MA4H0
  • Module name: Applied Dynamical Systems
  • Department: Mathematics Institute
  • Credit: 15

Content and teaching | Assessment | Availability

Module content and teaching

Principal aims

1. Review of basic theory: flows, notions of stability, linearization, phase portraits, etc. 2. 'Solvable' systems: integrability and gradient structure. 3. Invariant manifold theorems: stable, unstable and center manifolds. 4. Bifurcation theory from a geometric perspective. 5. Compactification techniques: flow at infinity, blow-up, collision manifolds. 6. Chaotic dynamics: horsehoes, Melnikov method and discussion of strange attractors. 7. Singular perturbation theory: averaging and normally hyperbolic manifolds.

Principal learning outcomes

This course will introduce and develop the notions underlying the geometric theory of dynamical systems and ordinary differential equations. Particular attention will be paid to ideas and techniques that are motivated by applications in a range of the physical, biological and chemical sciences. In particular, motivating examples will be taken from chemical reaction network theory, climate models, fluid motion, celestial mechanics and neuronal dynamics.

Departmental link

Module assessment

Assessment group Assessment name Percentage
15 CATS (Module code: MA4H0-15)
B (Examination only) 3 hour examination (April) 100%

Module availability

This module is available on the following courses:



Optional Core


  • Undergraduate Mathematics (MMath) (G103) - Year 3
  • Undergraduate Mathematics (MMath) (G103) - Year 4
  • Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
  • Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
  • Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
  • Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
  • Postgraduate Taught Mathematics (G1P0) - Year 1
  • Postgraduate Taught Mathematics (G1P0) - Year 2
  • Master of Advanced Study in Mathematical Sciences (G1PE) - Year 1