Gatabazi P, Mba J C, Pindza E
Department of Pure and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa.
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Rd., Hatfield, Pretoria 0002, South Africa.
Chaos. 2019 Jul;29(7):073116. doi: 10.1063/1.5096836.
The Fractional Gray Lotka-Volterra Model (FGLVM) is introduced and used for modeling the transaction counts of three cryptocurrencies, namely, Bitcoin, Litecoin, and Ripple. The 2-dimensional study is on Bitcoin and Litecoin, while the 3-dimensional study is on Bitcoin, Litecoin, and Ripple. Dataset from 28 April 2013 to 10 February 2018 provides forecasting values for Bitcoin and Litecoin through the 2-dimensional FGLVM study, while dataset from 7 August 2013 to 10 February 2018 provides forecasting values of Bitcoin, Litecoin, and Ripple through the 3-dimensional FGLVM study. Forecasting values of cryptocurrencies for the n-dimensional FGLVM study, n={2,3} along 100 days of study time, are displayed. The graph and Lyapunov exponents of the 2-dimensional Lotka-Volterra system using the results of FGLVM reveal that the system is a chaotic dynamical system, while the 3-dimensional Lotka-Volterra system displays parabolic patterns in spite of the chaos indicated by the Lyapunov exponents. The mean absolute percentage error indicates that 2-dimensional FGLVM has a good accuracy for the overall forecasting values of Bitcoin and a reasonable accuracy for the last 300 forecasting values of Litecoin, while the 3-dimensional FGLVM has a good accuracy for the overall forecasting values of Bitcoin and a reasonable accuracy for the last 300 forecasting values of both Litecoin and Ripple. Both 2- and 3-dimensional FGLVM analyses evoke a future constant trend in transacting Bitcoin and a future decreasing trend in transacting Litecoin and Ripple. Bitcoin will keep relatively higher transaction counts, with Litecoin transaction counts everywhere superior to that of Ripple.
引入分数阶灰色Lotka-Volterra模型（FGLVM）并将其用于对三种加密货币（即比特币、莱特币和瑞波币）的交易计数进行建模。二维研究针对比特币和莱特币，而三维研究针对比特币、莱特币和瑞波币。2013年4月28日至2018年2月10日的数据集通过二维FGLVM研究提供比特币和莱特币的预测值，而2013年8月7日至2018年2月10日的数据集通过三维FGLVM研究提供比特币、莱特币和瑞波币的预测值。展示了n维FGLVM研究（n = {2, 3}）在100天研究时间内加密货币的预测值。使用FGLVM结果的二维Lotka-Volterra系统的图形和李雅普诺夫指数表明该系统是一个混沌动力系统，而三维Lotka-Volterra系统尽管李雅普诺夫指数表明存在混沌，但呈现出抛物线模式。平均绝对百分比误差表明，二维FGLVM对比特币的整体预测值具有良好的准确性，对莱特币的最后300个预测值具有合理的准确性，而三维FGLVM对比特币的整体预测值具有良好的准确性，对莱特币和瑞波币的最后300个预测值都具有合理的准确性。二维和三维FGLVM分析都揭示了比特币未来交易的恒定趋势以及莱特币和瑞波币未来交易的下降趋势。比特币将保持相对较高的交易计数，莱特币的交易计数在各处都优于瑞波币。
