Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
This aims to be a course in nonlinear
dynamics and chaos with an interdisciplinary approach. The emphasis of
the course will be on general concepts, illustrated by applications to
problems in physics, chemistry and biology (ranging from mechanical
vibrations to biological rhythms). In each illustration, the scientific
background of the problem will be explained at an elementary level. The
emphasis will be on the analysis of the dynamical equations that model
the phenomena. The topic details are given below:
- First-order differential equations and their bifurcations.
- Limit cycles and their bifurcations.
- Phase plane analysis of flows on lines and circles.
- Lorenz equations and introduction to dynamical characteristics of
chaos.
- Iterated maps (eg. Logistic map, Tent map).
- Routes to chaos (in particular, period doubling).
- Concepts in renormalization, fractals, multifractals and strange
attractors.
- Spatiotemporal Chaos in extended nonlinear systems (eg. Coupled Map
Lattices).
- Illustrations from mechanical vibrations, lasers, biological rhythms,
superconducting circuits, insect outbreaks, chemical oscillators,
genetic control systems and chaotic waterwheels.
- S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications
To Physics, Biology, Chemistry, And Engineering (Studies in
nonlinearity), 01st edition, Westview Press (2001).
- Edward Ott, Chaos in Dynamical Systems, 02nd edition, Cambridge
University Press, (2002).
- M.Tabor, Chaos and Integrability in Nonlinear Dynamics: An
Introduction, 01st edition, Wiley-Interscience (1989).
