Psychology | Intro to Mathematical Psychology
P605 | 3498 | J. Townsend
Our goal is to present some basic aspects of linear and non linear
dynamics, at least at an introductory level. A sampling of likely
topics are: first vs. higher order systems, linear vs. non linear
systems, autonomous vs. non autonomous systems, phase space,
topological equivalence of orbits and introduction to symbolic
dynamics, bifurcation and catastrophe theory, definitions of chaos,
Hamiltonian and gradient systems, various kinds of stability, an
introduction to ergodic theory in 'deterministic' dynamic systems.
Poincare' maps, fractal structures and dimension, difference vs.
differential equations and maps vs. flows, Lyapunov exponents, strange
attractors, diverse kinds of oscillators, Morse-Smale systems,
Horse-shoe maps, averaging methods for non autonomous systems.
The lectures will be tuned to the mathematics, but approached more as
in physics as opposed to an axiomatic treatment. An occasional
important proof may be given. And considerable effort will be made to
make the mathematics intuitive to the extent possible and depending on
the individual student's background. Extant and potential
applications in cognitive science will be taken up, and I am eager to
learn of new applications. If time is available, some effort will be
expended on empirical data analysis, though that cannot dominate
lecture sessions. Since it will probably turn out that variation of
mathematical background in the audience will be large, I expect each
student to learn at his/her own level, each striving to learn as much
as possible at that particular stratum. The students will be
encouraged to avail themselves of the wonderful and relatively
inexpensive computer software for exploration of "dynamics country."