We study the dynamics of macroscopically-coherent matter waves of an

ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites

and demonstrate a novel type of spatio-temporal internal Josephson effect.

Using a discrete solitary mode of uncoupled spin components as an initial

condition, the time evolution of this many-body system is found to be

characterized by two dominant frequencies leading to quasiperiodic dynamics at

various sites. The dynamics of spatially-averaged and spin-averaged degrees of

freedom, however, is periodic enabling an unique identification of the two

frequencies. By increasing the spin-dependent atom-atom interaction strength we

observe a resonance state, where the ratio of the two frequencies is a

characteristic integer multiple and the spin-and-spatial degrees of freedom

oscillate in "unison". Crucially, this resonant state is found to signal the

onset to chaotic dynamics characterized by a broad band spectrum. In a

ferromagnetic spinor condensate with attractive spin-dependent interactions,

the resonance is accompanied by a transition from oscillatory- to

rotational-type dynamics as the time evolution of the relative phase of the

matter wave of the individual spin projections changes from bounded to

unbounded.