  Identifying the structural dependence between the cryptocurrencies and
predicting market trend are fundamental for effective portfolio management in
cryptocurrency trading. In this paper, we present a unified Bayesian framework
based on potential field theory and Gaussian Process to characterize the
structural dependency of various cryptocurrencies, using historic price
information. The following are our significant contributions: (i) Proposed a
novel model for cryptocurrency price movements as a trajectory of a dynamical
system governed by a time-varying non-linear potential field. (ii) Validated
the existence of the non-linear potential function in cryptocurrency market
through Lyapunov stability analysis. (iii) Developed a Bayesian framework for
inferring the non-linear potential function from observed cryptocurrency
prices. (iv) Proposed that attractors and repellers inferred from the potential
field are reliable cryptocurrency market indicators, surpassing existing
attributes, such as, mean, open price or close price of an observation window,
in the literature. (v) Analysis of cryptocurrency market during various Bitcoin
crash durations from April 2017 to November 2021, shows that attractors
captured the market trend, volatility, and correlation. In addition, attractors
aids explainability and visualization. (vi) The structural dependence inferred
by the proposed approach was found to be consistent with results obtained using
the popular wavelet coherence approach. (vii) The proposed market indicators
(attractors and repellers) can be used to improve the prediction performance of
state-of-art deep learning price prediction models. As, an example, we show
improvement in Litecoin price prediction up to a horizon of 12 days.
