Aconstructivetheoremisestablishedforgeneralizedsynchronization(GS)relatedtoC1diffeomorphictransformationsofunidirectionallycoupleddynamicalarrays.ThetheoremprovidessomeinterpretationsabouttheunderlyingmechanismofvariousGSphenomenainnature.Asadirectapplicationofthetheorem,achaos-basedsecureInternetcommunicationschemeisproposed.Moreover,acellularneuralnetwork(CNN)ofChen'schaoticcircuitswithGSpropertyisdesignedandstudied.NumericalsimulationshowsthatthisChen'sCNNhashighsecurityandisfastandreliableforsecureInternetcommunications.