  In this paper we fill the gap in understanding the non-stationary resonance
dynamics of the weakly coupled pendula model, having significant applications
in numerous fields of physics such as super- conducting Josephson junctions,
Bose-Einstein condensates, DNA, etc.. While common knowledge of the problem is
based on two alternative limiting asymptotics, namely the quasi-linear approach
and the approximation of independent pendula, we present a unified description
in the framework of new concept of Limiting Phase Trajectories (LPT), without
any restriction on the amplitudes of oscillation. As a result the conditions of
intense energy exchange between the pendula and transition to energy
localization are revealed in all possible diapason of initial conditions. By
doing so, the roots and the domain of chaotic behavior are clarified as they
are associated with this transition while simultaneously approaching the
pendulum separatrix. The analytical findings are corrobo- rated by numerical
simulations. By considering the simplest case of two weakly coupled pendula, we
pave the ground for new opening possibilities of significant extensions in both
fundamental and applied directions.
