Chimeras-States in the Distributed Systems in the Case of Multi-Valued Solutions. To the Statement of Possible Research Problems

Abstract

Nonlinear science has about a hundred years of rapid development. One of the new directions is the study of chimera solutions, i.e. solutions that exhibit significantly different solution behaviour in different regions of space or time. Just a few examples of such behavior have been studied in different systems. However, all examples of chimeras have been single-valued solutions. Recently, however, many nonlinear models of physical and social phenomena have multivalued solutions. It is conceivable that one of the possible directions for further research in chimera science is to allow multivalued solutions to be considered. The paper is devoted to describing some possible research settings in this area. Some modifications of existing models are also proposed. The interesting class of such objects is the models with strong anticipation (models with advanced arguments). Furthermore, some problems of computational theory and mind with such models are discussed.