Non-linear Non-Autonomous Dynamical System and R-Tipping

A Mathematical Theory for Studying and Controlling the Disinformation System Dynamics connection between disinformation, defined as deliberate spread of false information, and rate-induced tipping (R-tipping), Noise-Inducement, Understanding Subjective Patterns. This study explores the connection between disinformation, defined as deliberate spread of false information, and rate-induced tipping (R-tipping), a phenomenon where systems undergo sudden changes due to rapid shifts in external forces. While traditionally, tipping points were associated with exceeding critical thresholds, R-tipping highlights the influence of the rate of change, even without crossing specific levels. The study argues that disinformation campaigns, often organized and fast-paced, can trigger R-tipping events in public opinion and societal behavior. This can happen even if the disinformation itself doesn't reach a critical mass, making it challenging to predict and control. Here, by Transforming a population dynamics model into a network model, Investigating the interplay between the source of disinformation, the exposed population, and the medium of transmission under the influence of external sources, the study aims to provide valuable insights for predicting and controlling the spread of disinformation. This mathematical approach holds promise for developing effective countermeasures against this increasingly prevalent threat to public discourse and decision-making. The possible extension on this model is to extend this equation by considering the influence on public opinion and opinion formation model in a continuous scale. There are something to consider like, assuming that some scriptics are converting into the exposed again when they is being finished and some other actually sustained in this category but divided by their values. From this model we can see that when the scriptic population actually start protesting in that case the information have been spaded to the more people so the information ireach increases and the network has been extended. Some of this skeptips can play . role in opinion formation. Using feedback loop it is possible to measure the weight of their opinion and the influence.