**Memoirs of the American Mathematical Society**

1998;
73 pp;
Softcover

MSC: Primary 34; 58;

Print ISBN: 978-0-8218-0783-5

Product Code: MEMO/134/637

List Price: $47.00

Individual Member Price: $28.20

**Electronic ISBN: 978-1-4704-0226-6
Product Code: MEMO/134/637.E**

List Price: $47.00

Individual Member Price: $28.20

# Cyclic Feedback Systems

Share this page
*Tomáš Gedeon*

Study of dynamical systems usually concentrates on the properties and
the structure of invariant sets, since the understanding of these is
the first step in describing the long time behavior of orbits of the
entire dynamical system. There are two different sets of problems
related to the study of dynamical systems. One, the study of the
dynamics in the neighborhood of the critical elements like fixed
points or periodic orbits, is relatively well understood. This volume
tackles the second set of problems, related to a global dynamics and
the global bifurcations.

In this volume the author studies dynamics of cyclic feedback systems.
The global dynamics is described by a Morse decomposition of the
global attractor, defined with the help of a discrete Lyapunov
function. The author shows that the dynamics inside individual Morse
sets may be very complicated. A three-dimensional system of ODEs with
two linear equations is constructed, such that the invariant set is at
least as complicated as a suspension of a full shift on two symbols.
The questions posed are perhaps as significant as the reported
results.

#### Readership

Research mathematicians and graduate students interested in the structure of attractors (and repellors); biologists; electrical engineers.