Modeling cryptocurrencies transaction counts using variable-order Fractional Grey Lotka-Volterra dynamical system

Fractional Grey Lotka-Volterra Model with variable order is introduced and used for modeling the transaction counts of three cryptocurrencies namely Bitcoin, Litecoin and Ripple. Bitcoin and Litecoin then both three cryptocurrencies transaction counts are modeled in 2 and 3-dimensional framework respectively. Dataset include transaction counts of cryptocurrencies of interest. The 2-dimensional model uses Bitcoin and Litecoin transactions from April, 28, 2013 to February, 10, 2018. The 3-dimensional model uses transactions from August, 7, 2013 to February, 10, 2018. The actual values and the model values of n-dimensional model n={2,3} are displayed. The Mean Absolute Percentage Error (MAPE) suggests a high accuracy of the 3-dimensional Variable-order Fractional Lotka-Volterra model (VFGLVM) for the overall model values of Bitcoin and a reasonable accuracy for both model values of Litecoin and Ripple. The 2-dimensional VFGLVM has a good accuracy for the overall forecasting values of Bitcoin and a reasonable accuracy for the forecasting values of Litecoin. By analysing values of Lyapunov exponents and patterns of the corresponding Lotka-Volterra models, the 2 and 3-dimensional models show a chaotic behavior. Forecasting values indicate a future slight linear increase in transacting Bitcoin and a future decreasing transaction of Litecoin and Ripple. Bitcoin will keep relatively higher transaction counts and Litecoin transaction counts will be everywhere higher than that of Ripple.