Liu process is a type of fuzzy process. It is a fuzzy counterpart of Brownian motion. In this paper, the continuity property of Liu process is studied. It is proved that almost all Liu paths are Lipschitz continuous.

In this paper, the adaptive control design is investigated for chaos synchronization of two identical hyperchaotic Liu systems. First, an law with inputs proposed based on Lyapunov stability theory. Secondly, other schemes are obtained a further analysis law. Finally, numerical simulations presented to validate effectiveness and correctness these results.

A generalization of the method of Chu, Liu and Mehrmann [7] for the computation of the Hamiltonian real Schur form is presented. The new method avoids some of the difficulties that may arise when a Hamiltonian matrix has tightly clustered groups of eigenvalues. A detailed analysis of the method is presented and several numerical examples demonstrate the superior behavior of the method.

We consider the exact rogue periodic wave (rogue on background) and solutions for Chen–Lee–Liu equation via odd-th order Darboux transformation. Then, multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research data-driven wave, breather soliton of well-known equation. Especially, learned first time solve partial differential In addition, using image simulat...

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