Stability, in Covolution, denotes the basin-relative resilience of an informational pattern, specified at three parameters: a description level L (the resolution at which identity is defined), a timescale τ (the horizon over which persistence is asserted), and a noise scale σ (the amplitude of perturbations the pattern must absorb). A pattern is stable when perturbed trajectories recur within a neighborhood of an attractor over τ, with basin depth ΔV > σ at level L.
Stability is therefore a triple — stable(L, τ, σ) — not an absolute property.
Co-stability is stability that obtains only under sustained organism↔symvironment coupling: severing the coupling collapses the basin even when its internal regulatory loops remain intact. Co-stability has two failure modes. The first is acute uncoupling, in which the basin disappears as soon as the recursion is broken. The second is Cybernetic Attractor Decay (CAD): a slow structural deformation of the landscape itself under sustained coupling, in which basins flatten, separatrices erode, adjacent attractors merge, and ΔV progressively falls toward σ. CAD is loss of structural stability manifesting as eventual loss of basin stability — the geometry of viability decays while the organism is still trying to live within it.
Dimensions of stability and their CAD failure modes
| Dimension | What it specifies | CAD failure mode |
|---|---|---|
| Description level (L) | Resolution at which identity is defined (molecular, network, cellular, phenotypic) | Fine-grained patterns dissolve into coarse-grained noise; identity blurs across levels |
| Timescale (τ) | Horizon over which recurrence is asserted | Characteristic return time lengthens, then exceeds biological tolerance |
| Noise scale (σ) | Amplitude of perturbations absorbed without leaving the basin | Effective σ rises (damage accumulation) while ΔV falls; eventually ΔV < σ |
| Basin geometry | Bounded neighborhood toward which trajectories converge | Basin flattens, narrows, merges with neighbors; separatrices lower |
| Recursive coupling | Stability sustained by organism↔symvironment loop | Coupling weakens; co-stability decomposes into unstable component parts |
| Path dependence | Memory and prior trajectory bias current persistence | Memory degrades — epigenetic drift, immunological forgetting, mitochondrial heteroplasmy |
| Self-maintenance | Internal feedback regenerates the pattern | Loop gain drops; correction lags behind perturbation rate |
| Structural robustness | The landscape itself is robust to parameter drift | Bifurcations occur: old attractors vanish, pathological ones appear (senescence, fibrosis, tumor states) |
댓글 0