# Spatiotemporal Modeling of the Smart City Residents' Activity with Multi-Agent Systems
## 4 Model City
The study also examined the influence of some strong \"positive\" or \"negative\" leaders, the impact of the adopted function modifying the traits of the agents (linear, reinforcing, diminishing), as well as specific spatial problems in the model city. In the research, the authors adopted four analytical scenarios:  
* City functioning normally;
* The problem of spatial development of the \"empty\" seventh district;
* The problem of revitalizing a factory going into liquidation;
* The problem of changing the development of the model city's central square (market). Each of the scenarios is associated with the engagement of a specific group of residents (e.g., the elderly, the less affluent, or the residents of a given part of the city). Each agent is characterized by the \"susceptibility\" parameter, which determines the probability of an agent taking part in the social debate, demonstration, or protest. This characteristic is determined on the basis of the agent's other parameters, such as age, education, family, wealth, the level of identification with the city, and so forth. What is key, however, is a given agent's place of residence and the proximity (spatial or social) to the place where a problem, such as the revitalization of a district or the demolition of a controversial town hall, occurs. \"Ordinary\" agents engage (with a certain probability) in social life after work or on weekends. Only agents representing the \"strong leaders\" always remain in the conflict places. These agents do not change their level of involvement or trust during the interaction. For positive leaders, it is 1.0, while it is 0.0 for negative ones. Making use of the devised multi-agent system and the GAMA toolset environment, 3650 computational epochs were carried out. The characteristics of individual agents changed in each iteration because of contacts with individual actants (residents and spatial objects). Using GIS tools, the resulting data were subjected to spatial aggregation analyzing the change in the average level of trust of agents residing in a given district of a model city. First, the authors of the article made calculations, the purpose of which was to check how the particular trust parameter modifying functions works (Figures 4 and 5). Figure 4: The attractor activity and the level of mutual social trust in a model city through a simulated time of 10 years in the presence of 20 strong positive leaders. In Figure 4, one can observe the comparison of the attractor's activity and the level of mutual social trust in a model city through a simulated time of 10 years in the presence of 20 strong positive leaders. All plots rise steadily, but with slightly different slopes. Moreover, in the period of attractors' activeness (days 1200-2400), the curves are moving away from each other. The results indicate that there are differences between individual attractors, which results from various geospatial settings. In Figure 5, one can observe the comparison of the fan-idol and fan-anti-idol relations on the level of mutual social trust in a model city through a simulated time of 10 years in the presence of 20 strong positive leaders. What is interesting is that up to the 1600-ish day of simulation (four years and four months), the inactivity of the fan-idol and fan-anti-idol relations seems to be stronger. However, after that, the activity of the relations begins to be stronger, and at the end, after 10 years, the mutual trust is 0.4% stronger, compared to the inactivity of the relations. To sum up, the analysis of various attractors and various functions modifying confidence shows us minor differences, which result from the differences characteristic for a given area, rather than differences in the algorithm used. The variants of analytical simulations implemented are presented below.