chemart / random-catalytic-networks

hub:
  repo_type: generator
  builtin: random-catalytic-networks
  tags:
  - banzhaf-yamamoto
chemistries:
- id: random-catalytic-networks
  name: Random catalytic reaction networks
  intuition: 'The null model the more elaborate chemistries all instantiate. Species have no internal
    structure at all; instead, for every pair, a randomly drawn coefficient says how strongly that pair
    catalyses the production of a third. With a dilution flux, the system settles onto a stable fixed
    point; in sparse networks only a mutually-catalysing subset survives there and the rest dies out.
    Because it contains the replicator and Lotka-Volterra equations as special cases, it is the baseline
    against which structured chemistries have to justify their structure.

    '
  origin: Stadler, Fontana & Miller, 1993
  book: 7.2.9
  refs:
  - '[792]'
  family: evolutionary-dynamics
  kind: generator
  constructive: false
  S:
    repr: n abstract species X_1..X_n with no internal structure
    definition: explicit
  R:
    definition: explicit
    arity: 2
    scheme: X_i + X_j --alpha^k_ij--> X_i + X_j + X_k (both reactants catalytic)
    notes: x_k' = sum_ij alpha^k_ij x_i x_j - x_k phi(t), with phi = sum_ij a_ij x_i x_j and a_ij = sum_k
      alpha^k_ij
  A:
    reactor: ode
    dilution: non-specific dilution flux phi
  params:
  - name: n
    type: int
    default: 10
    min: 2
    max: 60
    role: structural
    meaning: number of species
  - name: density
    type: float
    default: 0.1
    min: 0
    max: 1
    role: structural
    meaning: probability that a given reaction X_i + X_j -> X_i + X_j + X_k exists; sparse to dense
  - name: allow_direct_replication
    type: bool
    default: false
    role: structural
    meaning: allow k = i or k = j; the book's interesting case forbids direct self-replication
  - name: alpha_distribution
    type: enum
    default: uniform
    choices:
    - uniform
    - exponential
    role: kinetic
    meaning: 'distribution of the rate alpha of an existing reaction: uniform on [0, 1) or exponential
      with mean 1'
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - flow
  fidelity: book+decisions
  decisions:
  - The book gives the reaction scheme, the ODE and the direct-replication switch, but not how alpha is
    drawn. Each existing reaction gets alpha from `alpha_distribution` (default uniform on [0, 1)).
  - Reactions are sampled per unordered reactant pair {i, j}. In the ODE the ordered terms alpha^k_ij
    and alpha^k_ji describe the same reaction, so one rate per pair loses nothing. The dilution phi is
    outflow = 'constant-total'.
  phenomena:
  - convergence to a stable fixpoint (interior when the network is dense; in sparse networks only a mutually
    catalytic subset survives) - later recognised as a chemical organisation
  - contains the replicator and Lotka-Volterra equations as special cases
  notes: 'The structural template that the matrix chemistry, the automata reaction and AlChemy all instantiate:
    Chemart''s canonical ''null model'' generator for benchmarking organisation-finding code.

    '