Has anyone considered that recessions are just lotka volterra cycles due to fuel resource depletion? Or has this been completely ignored by all economists for hundreds of years?
I don't know that anyone's used a Lotka Volterra framework: it's not an obvious choice, but it might make for a novel(ty) article. Nevertheless, yes, it's a well-established observation that historically, surges in oil prices have been part of triggering global economic downturns.
But that's just oil prices. So it's only during the oil age, which is now ending.
Historically, for the last couple of centuries, most of our energy has been implicitly and explicitly subsidised: implicitly by the huge externalities of fossil fuel combustion. The direct consequence of that is that fuel expenditure play an inefficiently large role in the global economy. And that means that rapid changes in global fuel prices have had a very destabilising effect on the global economy.
But there are two major changes coming:
It's not hard to see the transition to clean energy being one in which energy's role in the global economy diminishes, as externalities get priced in, and as energy efficiency consequently becomes much more cost-competitive.
Furthermore, a very large proportion of clean energy (hydro, wind, PV) has very low operating costs; whereas dirty energy has much much higher operating costs.
So for those two reasons, when we move from dirty energy to clean energy, the global economy will become much less coupled to changes in short-run marginal costs of energy.