Economies do not necessarily have to follow differential equations with highly volatile second derivatives.
In fact, historically, they haven't.
This is only possible because of the volatility of capital markets that lead to even higher volatility in production which leads to volatility in general markets which leads to volatility in capital markets again - there is a loop of unstable prices.
And this loop is the unique and defining feature of capitalism. It didn't exist before capitalism, and in experiments like those of the Soviet Union, it didn't exist either, because there were no capital markets at all.
What you're describing is a behaviour of capital markets, but due to a lack of perspective it's described as a behaviour of economies in general - and it isn't.
Basically every time varying system, no matter how complex, can be thought of as a system of differential equations. Human systems of production -- any such system -- is a time varying system, and as such, probably has some cyclic behavior, instability, etc. somewhere inside.
The USSR experienced all sorts of issues like this, where the central management would first over supply something, then react by massively undersupplying it, then overreact in the other direction. It also experienced a total collapse. It makes no sense to point to it as a model of stability.
(Also, as you read my message here, recall my claim isn't that communisms has cycles and capitalism doesn't, but everything does because there is no way to build an economic system that doesn't have -d^2/dt^2 terms showing up somewhere in it.)
Just because a set of differential equations has -d^2/dt^2 somewhere in it doesn't mean that it will lead to an increasing amount of instabilities that will eventually lead to spontaneous -30% economic activity.
The economy of the USSR, in aggregate, literally only ever suffered two recessions - one in 1963 due to political instability (which was a very minor fall in GDP), and one at the beginning of WW2. The collapse of the USSR itself was a purely political issue - the USSR maintained growth right up until its dissolution.
I understand your point, but it is a case of diagnosing a second-order effect but not taking into account it's actual impact. Outside of capitalism, there were not really any economic systems that had such gigantic vorticity that they would spontaneously enter disastrous depressions.
Those cycles that you diagnosed, for example, eventually ended up by either a worker lying to stop the cascade, or someone at the planning office realizing the issue. They never snowballed into a Great Depression, because that simply could not happen. The reason the behaviour of unrestrained vorticity is possible in capitalism is because of capital markets. Without capital markets, or an equivalent, the behaviour you are diagnosing is inevitably dampened.
Think about it like a PID loop - there is a -d^2/dt^2 term in it, the D-loop term. But because of the I-term and the P-term, if you tune it correctly, general error always goes down over a full wavelength. Capital markets allow the D-term to overpower the loop.
In fact, historically, they haven't.
This is only possible because of the volatility of capital markets that lead to even higher volatility in production which leads to volatility in general markets which leads to volatility in capital markets again - there is a loop of unstable prices.
And this loop is the unique and defining feature of capitalism. It didn't exist before capitalism, and in experiments like those of the Soviet Union, it didn't exist either, because there were no capital markets at all.
What you're describing is a behaviour of capital markets, but due to a lack of perspective it's described as a behaviour of economies in general - and it isn't.