A dynamical system, composed of the local duality scheme, the most general Venezianotype formula (the global duality) and an asymptotic convergence condition and being able to determine Born amplitudes for some meson-meson scattering, is studied in connection with the Caldi-Pagels idea to resolve the p-π puzzle that how can the p and π be members of a quark model U(6) 36 and the π be a Nambu-Goldstone boson satisfying the PCAC.