Attachment styles as coupling patterns

Attachment theory (Bowlby, Ainsworth, Mikulincer & Shaver) describes stable priors for how a mammal regulates arousal in close coupling. In FPE terms, attachment is not a separate module — it is learned defaults for \(\Phi\), \(\mathcal{D}_{KL}\), \(\Gamma\), and \(P_{in}\eta\) in dyads that function as co-regulatory substrate.

Secure base ≈ high \(\Phi\), low \(\Gamma\)

A secure attachment figure provides:

Predictable co-regulation → infant/adult spends less \(P_{in}\) on alarm; phasic spikes are shorter.
Accurate modelling → caregiver’s \(Q\) tracks child’s state → low \(\mathcal{D}_{KL}\) across the blanket.
Repair after rupture → \(\Gamma\) spikes are resolved; conflict set \(C\) stays small.

Secure adults approximate fractal coherence: relational \(\Phi\) supports cellular \(\Phi\) (sleep, HPA tone, immune function — Porges, McEwen).

Insecure patterns as term skews

Style	Folk label	Numerator	Denominator	Fractal
Anxious	Protest, cling	\(P_{in}\) mobilised but low \(\eta\) (protest, pursuit)	High \(\mathcal{D}_{KL}\) (“abandonment imminent”)	\(\Phi\) feels fragile → hyper-monitor partner
Avoidant	Withdrawal	Suppressed phasic \(P_{in}\); tonic may look “fine”	Self-\(\mathcal{D}_{KL}\) (needs minimised in model)	\(\Gamma\) avoided by distance; \(\Phi\) not co-regulated
Disorganised	Approach–avoid	Conflicting \(P_{in}\) commands	Model incoherent → high \(\mathcal{D}_{KL}\)	Often trauma: \(\Psi\) or caregiver \(\Phi\) was threat

Anxious attachment

Mechanism: \(\mathcal{D}_{KL}\) about partner availability stays high; agent pays continuous prediction-error tax.
Behaviour: checking, jealousy, emotional escalation — low-\(\eta\) aggression to force coupling signal.
FPE read: not “too loving” but expensive modelling + poor boundary specification.

Avoidant attachment

Mechanism: boundary maintained by decoupling rather than assertion; appears low-aggression but pays inward cost.
Behaviour: stonewalling, “I’m fine,” intimacy as threat.
FPE read: \(\Gamma\) reduction by shrinking the coupled graph — stable until \(\Phi\) needs co-regulation (illness, grief).

Disorganised attachment

Mechanism: caregiver was both shelter and threat → ISM cannot settle \(\mathcal{D}_{KL}\) about closeness.
FPE read: simultaneous drive to raise and lower \(\Gamma\); highest allostatic load when triggered.

Internal working models = priors on \(Q\)

Bowlby’s internal working model is the attachment prior on generative models of self and other:

“Am I worth \(P_{in}\) spent on my boundary?”
“Will honesty raise or lower \(\Gamma\) with this figure?”
“Is \(\Psi\) reliable?”

Therapy that updates attachment is, operationally, Bayesian model revision on those priors — lowering \(\mathcal{D}_{KL}\) about what closeness costs.

Pairings (common traps)

Dyad	Attractor
Anxious–avoidant	Pursuer raises \(\Gamma\); withdrawer raises \(\mathcal{D}_{KL}\) by silence → classic friction cycle
Anxious–anxious	Escalation arms race; both pay high \(P_{in}\), low \(\eta\)
Avoidant–avoidant	Low \(\Gamma\) surface, high latent \(\mathcal{D}_{KL}\); rupture on crisis

Interruption

Restore \(\Phi\): sleep, safety, somatic regulation before “relationship skills.”
Raise \(\eta\) on \(P_{in}\): observable + consequence, not protest script.
Lower \(\mathcal{D}_{KL}\): name needs and fears as hypotheses, test against behaviour.
Lower \(\Gamma\): repair rituals; if repair impossible, exit may be the \(\Gamma\)-optimal move.