Purpose <p>The article examines the problem of modeling wave phenomena in social networks or biophysical processes following the invasion of active alien content. During information attacks, epidemics, and the introduction of invasive species, explosive trends begin to pulsate and decay oscillatorically. When aggressively fake content is deliberately introduced and its dissemination is supported within social communication networks, transient oscillatory modes of activity emerge. Invasive processes in a&#xa0;population that slowly develops resistance subside due to adaptively generated countermeasures.</p> Methods <p>We propose three new models of aggressive invasion scenarios based on delay differential equations. The equations formalize various options for threshold-based regulation of the reproductive process and the activation of resistance from the biotic environment. The delay values in our models have different reproductive and adaptive interpretations.</p> Results <p>Modeling shows that when the reproductive efficiency of externally introduced content reaches an extreme value, stable equilibrium or oscillatory regimes of emotional contagion in the social network are not realized. After a&#xa0;series of brief wave peaks such allogenic foreign materials are eliminated from the environment.</p>