Exploring Self-Determination Theory through Mathematical Modelling

This code generates three sets of data representing different mathematical models of autonomy, competence, and relatedness over a specified time interval.

Linear Model: The linear functions for autonomy, competence, and relatedness depict a steady increase over time. Each function follows a straight line with a positive slope, indicating a linear relationship between time and satisfaction level for each psychological need.
Exponential Model: The exponential functions for autonomy, competence, and relatedness exhibit exponential growth patterns. As time progresses, the satisfaction level for each need increases at an accelerating rate, resulting in a curve that steepens over time.
Logistic Growth Model: The logistic growth functions for autonomy, competence, and relatedness represent a sigmoidal curve, characterized by an initial rapid growth phase followed by a gradual approach towards a saturation point. These functions reflect the idea that psychological needs may experience rapid development initially but eventually reach a limit as they approach their maximum satisfaction levels.
The plotted graphs visually represent the evolution of autonomy, competence, and relatedness according to each mathematical model. The x-axis represents time, while the y-axis represents the satisfaction level of each psychological need. The legend in each plot identifies which curve corresponds to autonomy, competence, or relatedness.

Overall, this code provides a visual comparison of different models of Self-Determination Theory, offering insights into how these psychological needs may evolve over time according to various mathematical assumptions.