MATHEMATICAL MODELING OF THE DYNAMIC BEHAVIOUR OF REINFORCEMENT THEORY: A NOVEL APPROACH

This study develops a mathematical model using a system of differential equations to describe the dynamics of reinforcement and punishment on behaviour over time. The model incorporates three variables: behaviour, reinforcement, and punishment, with equations governing the evolution of each. Stability analysis identifies two equilibrium points: one for stable positive behaviour and another for negative behaviour. Local stability analysis shows that positive reinforcement promotes behaviour growth, while excessive punishment leads to decay. Global stability analysis confirms that the system tends toward equilibrium, regardless of initial conditions, indicating predictable long-term behaviour. The findings highlight the importance of balancing reinforcement and punishment, with implications for optimizing teaching and behavioral strategies to foster positive outcomes in educational settings.