The review of the main existing approaches to consciousness in the literature indicates that consciousness is multileveled and that humans have an ability to experience a wide range of its various states. The common views of the main approaches to consciousness are identified and considered in a three-dimensional model of states of consciousness developed by Kokoszka. This model is then described and discussed using a mathematical terms of dynamic systems theory. Since mathematics is an accepted tool for the description of the physical world, the congruence of psychological and mathematical models is understood as a meaningful support to the psychological one. Connections of the models with artificial neural networks and some applications in psychology are considered.