Principle of enslavement

The principle of enslavement is a principle in the theory of synergetics . It says that the dynamics of subsystems is determined by system parameters.

example

Consider the two-dimensional dynamic system

${\displaystyle {\dot {x}}=-x-axy}$

${\displaystyle {\dot {y}}=-\gamma y+bx^{2}}$

With the demand for large , the solution for by arises ${\displaystyle \gamma \gg 1}$ ${\displaystyle y}$

${\displaystyle y(t)\approx {\frac {1}{\gamma }}bx^{2}(t)}$

This solution now states that the system is "enslaved" the system . H. follows the system . The theory of the center manifold offers a generalized solution method . ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle y}$ ${\displaystyle x}$

literature

• Hermann Haken : Synergetics . Springer-Verlag Berlin Heidelberg New York 1982, ISBN 3-540-11050-X