# Neural Network-Informed Lotka-Volterra Dynamics for Cryptocurrency Market Analysis
## 1 Introduction
That said, the rise of crypto has not been without skepticism. Several traditional financial institutions remain wary, viewing cryptocurrencies as speculative bubbles, rather than genuine innovations. Common criticisms include extreme price fluctuations, substantial energy demands, and relatively slow transaction speeds that hinder scalability and liquidity [9]. Some argue that neither Bitcoin nor blockchain has yet offered clear solutions to significant real-world problems. Nonetheless, regardless of whether these digital assets ultimately live up to their revolutionary promise, their current influence in the financial world is undeniable. As of today, the total market capitalization of all cryptocurrencies hovers around 3 trillion euros. A 2024 survey reported approximately 560 million active cryptocurrency users [10], highlighting the scale and reach of this emerging ecosystem. Unsurprisingly, the scientific community has taken a growing interest in cryptocurrencies, particularly through the lenses of complex systems and network theory. A considerable body of work has focused specifically on Bitcoin--examining its transactional network [11; 12], price dynamics, and forecasting models [13; 14]. However, only a limited number of studies have addressed the broader crypto market as a whole or attempted to model its complex behavior at the systemic level [15; 16]. This study explores the behavior of cryptocurrency market shares by applying the Lotka-Volterra model to Bitcoin (BTC), Ethereum (ETH), and a combined group of alternative coins (ALTs). We compare BTC, ETH, and ALTs because they represent the three most significant and distinct segments of the cryptocurrency market. BTC (Bitcoin) is the original and dominant cryptocurrency, ETH (Ethereum) is the leading smart contract platform, and ALTs (altcoins) collectively capture all other cryptocurrencies, reflecting broader market trends and diversification. Given the dominance of a few major cryptocurrencies in total market capitalization, significant barriers to new entrants, and interdependent strategic behavior, the cryptocurrency market exhibits key characteristics of an oligopolistic structure. This justifies the application of competitive dynamics models, such as the Lotka-Volterra framework, to analyze the evolution of market shares and concentration. To determine the nonlinear interaction parameters within the system, we integrate a neural network trained on actual market data. This combined method effectively captures the competitive and cooperative dynamics between major digital assets. The estimated parameters from the neural network are then used to simulate the system's evolution over time. Overall, the approach offers valuable insights into the structural behavior and shifts within the crypto market. The primary contribution of this study lies in analyzing the evolution of market structure and concentration by utilizing concepts from the evolutionary theory of population biology and population dynamics. Specifically, this research forecasts and models market evolution by employing the Lotka-Volterra framework, which is traditionally used to describe the competitive interactions between species vying for a shared, finite resource [17]. The primary objective of the proposed methodology is to offer an alternative approach for estimating the concentration level of a market with significant entry barriers, such as the cryptocurrency market. The Lotka-Volterra model utilized in this study has been applied successfully in various fields beyond biology, providing reliable estimates of the dynamics [18] within the processes it describes. Furthermore, the methodology proposed here can be integrated with existing frameworks or even used as a benchmark to validate their evaluation outcomes in the context of cryptocurrency markets. Achieving the objectives outlined above would make significant contributions to both academic research and practical applications.