Behaviour Dynamics Model

This visual representation captures the evolution of a behavioral system modeled through a set of Ordinary Differential Equations (ODEs). The system comprises undesirable behaviors (U) and positive behaviors (P), both subject to dynamic influences.

The model is governed by the ODEs encapsulated in the function behavior_dynamics. The behaviors are modulated by parameters
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a,
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b,
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c, and
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d, reflecting the dynamics of amplifying positive behaviors and diminishing undesirable behaviors. The intentional effort, represented by the functions
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(
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)
f(t) and
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(
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)
g(t), introduces intentional influences on the system. In this specific scenario, the intentional effort is exemplified by a sine function, but this can be tailored to mirror the intentional dynamics relevant to a particular context.

The time evolution of the system is depicted on the plot, with the x-axis representing time and the y-axis representing the levels of undesirable and positive behaviors. The initial conditions, set at the beginning, define the starting point of the system, with initial undesirable behaviors and positive behaviors represented by the values [1, 0].

The 'Undesirable Behaviours (U)' and 'Positive Behaviours (P)' lines on the graph illustrate the changing dynamics over time. The intentional effort, reflected in the intentional functions, contributes to the modulation of these behaviours. The plot provides a visual narrative of how intentional efforts impact the balance between undesirable and positive behaviours over the specified time range.

The title, "Behaviour Dynamics with Intentional Modulation," encapsulates the essence of the visual representation, emphasising the interplay between inherent behavioural dynamics and intentional efforts to shape the trajectory of undesirable and positive behaviours. This visualisation serves as a valuable tool for understanding how intentional interventions influence the evolution of a dynamic behavioural system.