In this paper, the finite-time bipartite consensus (FTBC) problem is investigated for the multiagent system (MAS) with detail balanced structure. To realize FTBC of MAS, a unified protocol framework is developed. Some criteria are established for realizing FTBC. It is worth noticing that estimations of settling time can be given in form of mathematical expression. The unified framework can bring in various protocols by choosing different parameters, which extends previous results. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of corresponding theoretical results. INDEX TERMSFinite-Time bipartite consensus; Filippov solutions; Detail balance digraph; Structurally balanced signed graph; Weighted signed average consensus; Settling time.

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In this paper, the homotopy analysis method is proposed to solve a class of holling model with the functional reaction. The model is characterized with the nonlinear equations in the denominator and it is difficult to obtain the closed approximation solutions. The series solutions of the model are obtained and the results show that the presented method is efficiency and simplicity. The convergence of this algorithm is also proved.

The finite-time stabilization problem of nonlinear systems is investigated in this paper. Firstly, to improve the precision of settling time of nonlinear system, a new finite-time stability theorem is established, and a higher precision settling time is derived from it. Moreover, by theoretical derivation, we prove that the corresponding settling time is more accurate than the existing results. Secondly, as an application, a new class of finite-time protocol framework, which unifies continuous protocol and discontinuous ones into a uniform formula, is designed to solve the finite-time stabilization problem of the general neural network system, and it can bring to a continuous control protocol and a discontinuous control protocol through choosing different design parameters. It is shown that the convergence rate is improved and also the corresponding settling time is upper bounded by some positive constant independent of initial conditions, which makes it convenient and flexible to adjust the settling time by adjusting design parameters. Finally, two numerical examples are provided to illustrate the effectiveness of our theoretical results. INDEX TERMSFinite-time stability theorem; Filippov solution; General neural networks; Lyapunov function; Settling time function; Upper bound of settling time

In this paper, we apply the homotopy Analysis Method (HAM) to obtain approximation analytical solutions of Ablowitz-Ladik-Lattice, that illustrate the validity and the great potential of the HAM in solving discrete Ablowitz-Ladik-Lattice. The results show that the proposed method is feasible and convenient.