Breakdown of autoresonance due to separatrix crossing in dissipative systems: From Josephson junctions to the three-wave problem.

Optimal energy amplification via autoresonance in dissipative systems subjected to separatrix crossings is discussed through the universal model of a damped driven pendulum. Analytical expressions of the autoresonance responses and forces as well as the associated adiabatic invariants for the phase space regions separated by the underlying separatrix are derived from the energy-based theory of autoresonance. Additionally, applications to a single Josephson junction, topological solitons in Frenkel-Kontorova chains, as well as to the three-wave problem in dissipative media are discussed in detail from the autoresonance analysis.