Slow manifolds of some chaotic systems with applications to laser systems (Q2709996)

The authors study equations for the slow manifold in several fast-slow dynamical systems. The key idea is that the slow manifolds are locally characterized by the position of the eigenvectors of the Jacobian matrix.NEWLINENEWLINENEWLINEA system of equations can be obtained (this was developed in an earlier paper) by expressing that the slow manifold is locally defined by being orthogonal to the system's left fast eigenvectors. The fast eigenvectors are those that correspond to the dominant real, negative eigenvalues. Alternatively, in this paper the tangent system's slow right eigenvectors can be used. This method allows to give a geometrical characterization of the attractor of a chaotic system; this restores a part of the deterministic property of the systems that was lost because of the sensitivity to initial conditions.NEWLINENEWLINENEWLINEAs typical (and important) examples the authors study the Lorenz system, Chua's model and several laser systems.