In connection with the technological progress of mankind, the assessment of the impact of radiation on the human body and in particular on the brain and its cognitive functions is an important task. First of all, the relevance of such a task arises from the introduction of radiation therapy for brain tumors and radiation protection during manned flights beyond the Earth's magnetosphere. The crew and passengers on high-altitude air flights are also exposed to cosmic rays to some extent. We developed a neural network model of working memory based on biophysical conductivity to study radiation-induced disorders and found how known dose-dependent changes in the main parameters of neurons affect the spatiotemporal dynamics of the network. It turned out that radiation-induced changes in the properties of synaptic receptors lead to a loss of stability of specific activity patterns. This instability occurs at very low doses of heavy charged ions, but not for protons.