title: Invariant integral and the transition to steady states in separable dynamical systems
abstract: We show that the transition between fixed points in a separable dynamical system is fully described by an invariant integral. We discuss in detail the case of a system with two temporal variables with bilinear coupling, where the new stable state is attained asymptotically through spiraling into the fixed point. Through the invariance, it is possible to establish conditions for the control parameter that permit a (targeted) transition in finite time and without relaxation oscillations.
authors.affiliation: Institut Non Lineaire de Nice, UMR 6618 CNRS-Universite de Nice-Sophia Antipolis, 1361 Route des Lucioles, F-06560 Valbonne, France.
authors.initials: GL
authors.lastname: Lippi
authors.initials: S
authors.lastname: Barland
authors.initials: F
authors.lastname: Monsieur