In this paper, the adaptive synchronization method of three coupled identical chaos systems is proposed. New generic criteria of global chaos synchronization and strict theoretical proofs are given. The unidirectional (bidirectional) coupled system will synchronize by adding three adaptive feedback gain equations. As an example, the three Rössler chaotic systems with unidirectional coupling are given to realize the adaptive coupled synchronization; at the same time, the three Lorenz chaotic systems donate the bidirectional coupling adaptive synchronization. This paper also extends the above adaptive synchronization method to secure chaos communications through the method of chaos masking. Based on the three coupled identical Lorenz chaotic systems, a novel method of chaos encryption is proposed, and the basic idea is that after encrypting two times in two transmitters and one receiver, information signal can be recovered exactly at the receiver end. In consideration of interfering random white noise, the results of encoding and decoding are simulated and analyzed for the multistage chaos synchronized system. By analyzing the characteristics of noise, this paper presents a de-noising method using wavelet transform. At last, a secure communications method for high amplitude information signal transmission based on chaotic masking is studied. With the MATLAB, the effects of signal de-noising could be demonstrated.

This work uses the collocation approximation method to solve a specific type of backward stochastic Volterra integral equations (BSVIEs). Using Newton’s method, BSVIEs can be solved using block pulse functions and the corresponding stochastic operational matrix of integration. We present examples to illustrate the estimate analysis and to demonstrate the convergence of the two approximating sequences separately. To measure their accuracy, we compare the solutions with values of exact and approximative solutions at a few selected locations using a specified absolute error. We also propose an efficient method for solving a triangular linear algebraic problem using a single integral equation. To confirm the effectiveness of our method, we conduct numerical experiments with issues from real-world applications.

In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a.

We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

Ethereum has become a significant trading platform for financial activities such as Dapps, ICOs, and DeFi. However, it has also become a hub for criminal activities such as fraud, money laundering, and illicit fundraising. The construction of fraud detection models employing machine learning techniques is currently a mainstream research direction. Nevertheless, existing studies face significant challenges, including class imbalance in data samples and a lack of model interpretability. In this content, this work proposes a novel explainable model for Ethereum illicit account detection, ETHIAD (Ethereum Illicit Account Detection). Firstly, we pre-process the dataset by ADASYN oversampling and Lasso feature selection, etc., to more efficiently achieve feature modeling of transaction structures. Then, the ETHIAD model is trained using the XGboost algorithm, with an accuracy, precision, recall, F1 score, and AUC value of 99.70%, 99.51%, 99.02%, 99.26%, and 99.45%, respectively, the model outperforms the existing SOTA model by 0.05%−1.1%. Finally, we introduce SHAP framework to analyze the key influencing factors of illicit accounts from multiple perspectives, and the conclusions strongly enhance the explainability of the model.