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is an example of weakly nonlinear oscillators, dynamical motif A conserved pattern of
i.e., small perturbations of the linear oscillator dynamical regimes for a reaction or group of
¨ x + x = 0. reactions.
Comment: Notice this is distinct from a device
in that the latter is not required to exhibit
Dym’s equation The nonlinear evolution
conservation. See also biochemical, chemical,
equation
u = 2(u −1/2 ) . functional, kinetic, mechanistic, phylogenetic,
t xxx
regulatory, thermodynamic, and topological
motives.
dynamic equilibrium In a chemical or bio-
chemical reaction, the continuous reaction of
dynamical system (1) The flow F of a vec-
sinistralateral and dextralateral sets of coreac- t
tor field X on a manifold M; i.e., F : M → M
tants, such that no net change in the concentra- t
is a one-parameter group of diffeomorphisms,
tions of each members of both sets occurs.
F = F ◦F , and satisfies the differential equa-
Comment: What determines which direc- t+s t s
tion
tion of a reaction forward or backward will d
predominate is the relative concentration of F (x) = X(F (x)) .
t
t
dt
reactants forming the two sets of obligatorily co-
(2)(autonomous dynamical system) a pair
reacting species. High concentrations of one set
(M, X) where M is a manifold and X is a vector
will drive the chemistry in the direction which
field over M.An integral curve γ : R → X is
consumes the reactants of that set, until the two
such that
sets are in equilibrium. See also dextralateral,
direction, formal reaction equation, microscopic ˙ γ = X ◦ γ
reversibility, product, rate constant, reversibility, where ˙γ is the tangent vector to γ .
sinistralateral, and substrate.
(3)(non-autonomous dynamical system over
ˆ
ˆ
ˆ
M ) a dynamical system (M, X) over M = R ×
dynamic viscosity, η η η For a laminar flow of M such that X = ∂ + X(t, x), where X(t, x) is
ˆ
t
a fluid, the ratio of the shear stress to the velocity a time-dependent vector field over M.
gradient perpendicular to the plane of shear. See equilibrium point, first integral.

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