Lyapunov Functions and Venture Capital

In complex systems, it is not easy to even think about equilibrium. The functions that could explain certain phenomena seem too irrelevant or straightforward to explain the system configuration and behavior. Everything seems to be organic, unstructured, and emergent at the Venture Capital industry and early-stage investments. It is an industry tied to the technology cycles, innovation process, and economic volatility. As mentioned before, and as George Box said, all models are wrong; some are useful. I explored the Lyapunov functions, and I see an opportunity for application in startups and the risk capital world.??

Lyapunov created his theorems, models, and theories in a time dominated by mechanics and energy. His thinking about equilibrium was based on time and energy in a dynamic system. The two conditions required to find the Lyapunov function were enough to find equilibrium in systems and are valid in our times with social sciences applications.??

I can see some applications for this kind of model in the venture capital industry. Depending on the capital maturity ecosystems, the valuations at an early stage tend to grow or decrease without a clear state of equilibrium. In ecosystems like Silicon Valley, valuations rise all the time due to the competition between investors for the best deals. Every time investors increase their offers and decrease their expectations; they get in a cycle of growing valuations which eventually must find a maximum value or an equilibrium. The opposite happens in emergent countries where there are not enough investors. The few venture capitalists who exist tend to offer lower valuations because they have the bargaining power, creating a downward spiral of valuations affecting both companies and investment performance.?

The Lyapunov functions describe the impact of externalities and how they can affect the natural flow of the system. In this case, I can observe the influence of global venture capitalists coming to regions like Latin America and affecting the valuations trends. Global VCs interrupt the systems providing super-high valuations opposite to the low valuations trend in the system. This phenomenon makes it difficult to identify a Lyapunov function, but it does not matter that it could not exist.?

Lyapunov functions have a tremendous number of applications in several fields in modern days. Starting with regulatory and tax practices and organizational and individual complex systems. In the era of big data, the possibility of identifying and building predictions using Lyapunov theories is fascinating.?