A system and method for enabling and improving user engagement through responsive iterative and cyclic interaction using mobile devices, for the creation of, response to, or alteration of, notifications on public display screens. The invention includes computer hardware and software for implementing, by delivering notification content, notification type, and means of notification, an iterative or cyclic response by users responsive to sensed or observed real world events and computer system events. The inventions also includes systems for synthesizing user interaction originating on groups of mobile devices in order to, through responsive cyclic iterative interaction, create, respond to, or alter, at least two separate and separately sourced simultaneously occurring notifications on a public display screen or screens. The invention further relates to a system and method on computer hardware and software system display or notification means for enabling and improving user situational awareness, cognition, and response, by recognizing and delivering, for a response option, cyclic, iterative responses through to notifications on a display.