The first theory to dismantle with the help of patterns of chaos science is E. Tory Higgins’ theory of self-discrepancy and regulatory fit. The theory is described in detail in Higgins (1987, 1997, 2000). The following figure shows a simplified, systematic overview over the theory:

Both dynamics of Higgins’ preventive and preventive behaviour can be modelled as attractors or repulsors. They are extremes on a discrete-looped spectrum of phase transitions. The intermediate phase space may be seen as alternating between several behavioural options. Additionally, Higgins notes that people may have different behaviour with regard to different topics or contexts, and there may be priming or costs to the context transitions.

This theory thus qualifies as looped-discrete theory.

References

Higgins, E. T. (1987). Self-discrepancy: A theory relating self and affect. PsychologicalReview, 94(3), 319-340.
Higgins, E. T. (1997). Beyond pleasure and pain. American Psychologist, 52(12), 1280-1300.
Higgins, E. T. (2000). Making a good decision: Value from fit. American Psychologist, 55(11), 1217-1230.