# Neural Network-Informed Lotka-Volterra Dynamics for Cryptocurrency Market Analysis
## 1 Introduction  
Over the past decade, blockchain technology has rapidly emerged as a transformative force, with many experts predicting that it could reshape various aspects of modern society [1]. At its core, a blockchain is a decentralized, publicly accessible digital ledger [2]. While it is most commonly associated with cryptocurrencies--digital assets designed to function as a medium of exchange without the need for centralized oversight--it has far-reaching applications beyond that. Bitcoin, introduced in 2008 [2] under the pseudonym [PERSON] (whose identity remains unknown and may represent either an individual or a group), stands as the pioneer and most widely recognized cryptocurrency. By December 2024, Bitcoin's market capitalization soared to around 1.8 trillion euros [3], and it continues to maintain a strong market presence, currently valued above 1.4 trillion euros. The revolutionary concept introduced by [PERSON] not only sparked a dramatic surge in Bitcoin's financial value but also inspired the creation of thousands of alternative cryptocurrencies. Today, over 17,000 digital currencies exist, either directly based on Bitcoin'soriginal blockchain or built on modified versions. This number continues to grow steadily. Beyond cryptocurrencies, blockchain technology has found applications across various sectors [4], with decentralized finance (DeFi) emerging as one of the most prominent. A significant part of what has driven the success of cryptocurrencies is their strong focus on security and user privacy-features [5] that traditional financial systems often struggle to match. By utilizing advanced cryptographic protocols, digital currencies ensure the integrity of transactions and protect the anonymity of users. Additionally, the decentralized architecture behind most cryptocurrencies removes the need for central governing bodies [6], which not only reduces transaction costs but also improves efficiency and accessibility. Ethereum, one of the most prominent cryptocurrencies, has taken these innovations even further. It introduced smart contracts-self-executing agreements [6] coded directly onto the blockchain. These contracts automatically enforce their terms, offering greater transparency and eliminating the need for intermediaries. This breakthrough has significantly expanded the use cases for blockchain technology, pushing it beyond simple peer-to-peer payments into areas like decentralized finance (DeFi), gaming, and various Web3 applications. As of 8 April 2025, Ethereum's market capitalization stands at approximately 167 billion euros [7]. This marks a significant decline compared to December 2024, when its market cap was valued at around 401 billion euros. The distinct benefits of blockchain--particularly its security, transparency, and decentralized control--continue to fuel the rise of cryptocurrencies like Ethereum. As the technology matures and adoption spreads, it is likely to play an even more critical role in shaping the future of finance. Given Ethereum's open-source nature, decentralized framework, and history of high returns, it has become a prime focus for investors and researchers alike, sparking growing interest in forecasting its price dynamics and understanding its long-term potential. Cryptocurrencies have steadily gained prominence and are now playing an increasingly significant role in the global financial landscape. At their peak, the total market capitalization of digital assets approached 3 trillion euros, rivaling the valuations of some of the world's largest publicly traded companies. What once began as an experimental domain for a niche group of tech-savvy enthusiasts has evolved into a mainstream asset class. The launch of Bitcoin futures in 2017 marked a turning point, and the approval of spot Bitcoin ETFs in January 2024 further solidified crypto's presence in traditional financial markets. Initially driven by retail interest, the space has since attracted major institutional players [8], with many more expected to follow suit.