Algorithms And Theory Of BP Neural Network And Anomalous Stochastic Lattice Systems With A Caputo Fractional Time Derivative

This paper includes two parts. In part 1, we studied the theory and the application of BP Network Based on BFO Algorithm and PSO Algorithm. In part2, the asymptotic behavior of a stochastic lattice system with a Caputo fractional time derivative is investigated.BP neural network, whose full name is Back Propagation, the concept of which was firstly proposed in 1986, put forward by the group Rumelhart and McCelland.Look from the topology structure, the BP neural network can be built by the input layer, the hidden layer, and output layer. The multilayer feed forward network,according to the error back propagation algorithm, weakness has a wide range of applications in various fields such as biological, engineering, chemistry, and so on.To the steepest descent method as a learning rule, BP neural network may rely on the back propagation to real-time to adjust the network weights and threshold,so that the error sum of squares can be the least. Without knowing reaction equation of input-output model mapping relation, BP neural network can approximate any continuous nonlinear function, so it is widely used in many important fields.Though it has a lot of advantages, however, it also has a slow convergence speed,and can not guarantee convergence to the global optimal point. At the same time,to solve the problem of the number of the middle layer and its cell selection theory instruction and network instability in learning and memory, in this paper we use BFO bacteria foraging optimization algorithm and the improved PSO particle swarm algorithm to avoid the situation, in which the network may fall into local minimum, unable to converge to the global minimum point, to get a faster convergence speed.Fractional differential equations now play a central role in the modeling of anomalous di?usion processes. They arise naturally in a wide variety of applications such as physics, fluid mechanics, viscoelasticity, heat conduction in materials with memory, chemistry and engineering. Fractional di?erential equations with the fractional substantial derivative also appear in the transport equation of describing the time evolution of the PDF of a L?evy walk, which is a CTRW model with the spatiotemporal coupled PDFs of waiting time and jump length.The asymptotic behavior of a stochastic lattice system with a Caputo fractional time derivative is investigated. In particular, the existence of a global forward attracting set in the weak mean-square topology is established. A general theorem on the existence of solutions for a fractional SDE in a Hilbert space under the assumption that the nonlinear term is weakly continuous in a given sense is established and applied to the lattice system. The existence and uniqueness of solutions for a more general fractional SDEs is also obtained under a Lipschitz condition.