Let me nitpick you on the set-up.
ATinNM:

Starting with the thinking of Malthus the Belgium mathematician Pierre Francois Verhulst developed the Verhulst  Equation:

which was generalized and simplified by the American Robert May, who renamed it to the Logistic Equation:

x² = λx(1-x)

Where:

x is the starting population
x² is new population after  ...
λ as the rate of increase of that population, including, though abstracted, the resources consumed to sustain the population and its increase.

If the logistic equation follows from the Velhust equation as a discretization of a differential equation, with appropriate choices of the units of population and time, then lambda does not include "the resources consumed to sustain the population and its increase".

Write the Velhust equation as

dP = r P (1 - P/K) dt

Where K is where the resources needed to sustain the population come in, in the form of an "equilibrium population size"; r is the vegetative growth rate when resources are plentiful (therefore r is resource-independent); and dt is the time step involved in discretization of the differential equation. This means

P' - P  = r P (1 - P/K) dt

so

P' = P (1 + r - rP/K) dt

or

P' = (1 + r)dt P {1 - rP/[(1 + r)K]} dt

If you choose (1 + 1/r)K as the unit of population, setting P = x(1 + 1/r)K, you get

x' = (1 + r)dt x (1 - x)

and so

λ = (1 + r)dt

has more to do with the discretization of the Velhust equation than it does with the resource use.

Put this way, the λ = 3 bifurcation point indicates the point at which the discretization is too coarse to faithfully represent the Velhust equation.

Of course, in reality the logic of the model goes the other way: the logistic equation comes first and the Velhust equation is a continuum approximation to it, valid only if λ < 3.

But, in any case, the point about λ stands: the "resources" are implicit in the units of x, and λ has to do with the vegetative growth rate when the population is small and resources are not a constraint and so is resource-independent.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris