Introduction to the Modeling and Analysis of Complex Systems

60 CHAPTER 4. DISCRETE-TIME MODELS I: MODELINGand p l , respectively (0 ≤ p c ≤ 1; 0 ≤ p l ≤ 1; 0 ≤ p c + p l ≤ 1). This implies that1 − p c − p l = p n represents the popularity of neutral.Assume that at each election poll, people will change their ideological statesamong the three options according to their relative popularities in the previous poll.For example, the rate of switching from option X to option Y can be consideredproportional to (p Y − p X ) if p Y > p X , or 0 otherwise. You should consider sixdifferent cases of such switching behaviors (conservative to liberal, conservativeto neutral, liberal to conservative, liberal to neutral, neutral to conservative, andneutral to liberal) and represent them in dynamical equations.Complete a discrete-time mathematical model that describes this system, andsimulate its behavior. See what the possible final outcomes are after a sufficientlylong time period.Exercise 4.16 Revise the model of public opinion dynamics developed in the previousexercise so that the political parties of the two ideologies (conservative andliberal) run a political campaign to promote voters’ switching to their ideologies fromtheir competitions, at a rate inversely proportional to their current popularity (i.e.,the less popular they are, the more intense their campaign will be). Simulate thebehavior of this revised model and see how such political campaigning changesthe dynamics of the system.