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This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components.

The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors.

Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist.

The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

This paper examines and forecasts correlations between cryptocurrencies and major fiat currencies using Generalized Autoregressive Score (GAS) time-varying copulas. The authors examine to which extent the multivariate GAS method captures the volatility persistence and the nonlinear interaction effects between cryptocurrencies and major fiat currencies.

The authors model tail dependence between conventional currencies and Bitcoin utilizing a Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroscedastic model (GJR-GARCH)-GAS copula specification, which allows detecting the leptokurtic feature and clustering effects of currency returns distribution.

The authors' results show evidence of multiple tail dependence regimes, implying the unsuitability of applying static models to entirely describe the extreme dependence between Bitcoin and fiat currencies. Compared to the most common constant copulas, the authors find that the multivariate GAS copulas better forecast the volatility and dependency between cryptocurrencies and foreign exchange markets. Furthermore, based on the value-at-risk (VaR) and expected shortfall (ES) analyses, the authors show that the multivariate GAS models produce accurate risk measures by adding cryptocurrencies to a portfolio of fiat currencies.

This paper has two main contributions to the existing literature on cryptocurrencies. First, the authors empirically examine the tail dependence structure between common conventional currencies and bitcoin using GJR-GARCH GAS copulas which consider the leptokurtic feature and clustering effects of currency returns distribution. Second, by modeling VaR and ES, the authors test the implication of using time-varying models on the performance of currency portfolios, including cryptocurrencies.