Yu.А. Basistov, Yu.G. Janovsky
The dynamic model of the nonlinear viscoelastic element possessing associative and fading memory is offered. The model generalises known viscoelastic elements of Maxwell, Jeffrey and Voigt-Kelvin. The nonlinear mathematical model for simulating behavior of complex heterogeneous viscoelastic media is synthesised. The model consists of nonlinear viscoelastic elements with fading and associative memory, and synaptic connection between them in the form of integral Volterra operators. It is established that the offered model can be realized on a nonlinear dynamic neural network with associative and fading memory. It is shown that the known neural network of Hopfield is a special case of the offered model. The theorem of stability of the offered dynamic model is resulted. Identification of our model is made by algorithm "training with the teacher" and consists in a choice of elements relaxation matrix by mean of a minimum root-mean-square error between result of simulating and the required. The diagonal relaxation matrix is squares a relaxation times of separate viscoelastic elements. Other elements of this matrix characterize relaxation synaptic connection between viscoelastic elements. The model is realized in the form of the nonlinear integro-differential system equations. The integral part contains long-term memory of model, and a differential part - short-term memory.