In this paper, the (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation is studied by the bifurcation theory of dynamical system. Based on this theory, phase portraits of different topological structures of the equation are obtained, which clearly show all bounded orbits corresponding to the bounded traveling waves of the equation. Furthermore, the periodic wave solution of the (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation are obtained by calculating complicated elliptic integrals.

Energy prediction for different cluster structures is the basis for finding and predicting the global optimal structure of clusters. The current methods for predicting the energy of the ground state structures of different clusters include theoretical prediction methods and optimized simplified potential energy function methods. The accuracy of the theoretical prediction method is high, but its calculation amount is too large. Therefore, this paper proposes a PSO-BP neural network three-dimensional cluster energy prediction model based on atomic coordinates, and uses different types of Euclidean distances between atoms as input variables, and the energy of clusters with different structures as output variables. Select gold cluster Au20 and boron cluster B45-part of the sample data as the training set to build the model, and predict the rest of the samples, and finally get: the prediction accuracy of the PSO-BP neural network model is higher than that of the traditional BP neural network model. The cluster energy prediction model is feasible.

Consider the existence of a non-autonomous two-dimensional stochastic plate equation with linear memory term pullback the attractor on . Apply the Ornstein-Uhlenbeck process to deal with the random term, transform the original equation into a deterministic equation containing random variables, and then estimate its consistency by replacing the system solution with variables, and prove that the random dynamic system corresponding to the original system equation pullback the absorption set Existence, and finally proves the system's pullback asymptotically compaction , which leads to the existence of the pullback attractor of the original system.