As defined by Walker1 et al., “a ‘basin of attraction’ is a region in state space in which the system tends to remain (2004). In this basin of attraction system achieves its maximum possible performance based on combination of its state sets.
The basin is a set of states or configurations with the same functions and feedback: with basically the same identity. What is called a regime (or set of system states) is an identifiable configuration of that system with characteristic structures, functions, feedbacks, and therefore, identity that tend towards equilibrium; the equilibrium state is defined as an ‘attractor’ inn maintaining its stated performance. The basin acts as a basin of attraction: as long as the ball is in the basin (black dot), the system is in that regime; so a particular basin coincides with a particular regime.
The characteristics of the basin of attraction (the three aspects of resilience) is defined as three dimensional topography that has quantitative representation of relief (vertical and horizontal dimensions), usually using contour lines (of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value). While the black dot represent system state and its trajectory along the contour lines. In this three-dimensional framework the map is comparable to the effect of gravitational fields Einsteinian space (Walker, et al., 2004).
Three-dimensional basin of attraction is represented by:
L = latitude, the maximum amount system can be changed before losing its ability to recover
R = resistance, the ease or difficulty of changing the system
Pr = precariousness; the current trajectory of the system and how close it is currently to its `threshold’ or ‘tipping point’
Different basins exert force that can attract the system. This is critical when looking at how to move to a different, desired, system state. It may be difficult to get from “here to there” without dropping into an unwanted state due to its attractiveness and resilience.
Fundamentally the states of the system within the basin of attraction represented by:
- System elements
- Relationship of system elements
- Attributes (fixed and dynamic) of elements and relationship
- Both attributes and relationship are associated by function called variables
- Performance associated to variables
- Function and purpose; the function and interaction of each sub-systems in achieving its purpose
- Identity ; characteristics of system elements associated with sub-system and it properties