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Neural Network-Informed Lotka–Volterra Dynamics for Cryptocurrency Market Analysis

Author

Listed:
  • Dimitris Kastoris

    (Department of Management Science and Technology, University of Patras, 26504 Patras, Greece
    These authors contributed equally to this work.)

  • Dimitris Papadopoulos

    (Department of Management Science and Technology, University of Patras, 26504 Patras, Greece
    These authors contributed equally to this work.)

  • Konstantinos Giotopoulos

    (Department of Management Science and Technology, University of Patras, 26504 Patras, Greece
    These authors contributed equally to this work.)

Abstract

Mathematical modeling plays a crucial role in supporting decision-making across a wide range of scientific disciplines. These models often involve multiple parameters, the estimation of which is critical to assessing their reliability and predictive power. Recent advancements in artificial intelligence have made it possible to efficiently estimate such parameters with high accuracy. In this study, we focus on modeling the dynamics of cryptocurrency market shares by employing a Lotka–Volterra system. We introduce a methodology based on a deep neural network (DNN) to estimate the parameters of the Lotka–Volterra model, which are subsequently used to numerically solve the system using a fourth-order Runge–Kutta method. The proposed approach, when applied to real-world market share data for Bitcoin, Ethereum, and alternative cryptocurrencies, demonstrates excellent alignment with empirical observations. Our method achieves RMSEs of 0.0687 (BTC), 0.0268 (ETH), and 0.0558 (ALTs)—an over 50% reduction in error relative to ARIMA(2,1,2) and over 25% relative to a standard NN–ODE model—thereby underscoring its effectiveness for cryptocurrency-market forecasting. The entire framework, including neural network training and Runge–Kutta integration, was implemented in MATLAB R2024a (version 24.1).

Suggested Citation

  • Dimitris Kastoris & Dimitris Papadopoulos & Konstantinos Giotopoulos, 2025. "Neural Network-Informed Lotka–Volterra Dynamics for Cryptocurrency Market Analysis," Future Internet, MDPI, vol. 17(8), pages 1-22, July.
    • Handle: RePEc:gam:jftint:v:17:y:2025:i:8:p:327-:d:1709235
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    References listed on IDEAS

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    5. D. F. Papadopoulos & T. E. Simos, 2013. "The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge‐Kutta‐Nyström Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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