Modeling Threshold Effects of Rapid Collapse and Devastating Invasion Outbreaks in Biophysical Systems

A methodology for hybrid computational modeling for special crisis cases is developed. Extreme phenomena and transient processes occurring suddenly in various biophysical systems are explored. The methods of mathematical biophysics require flexible expansion due to situationally activated intense influencing factors, which has been demonstrated well by the COVID-19 pandemic with the effects of virus superspreading and the instant launch of new COVID waves. Several economically important and hard-to-predict extreme biophysical processes with very rapidly changing evolutionary stages are compared. A classic example of a phenomenon disrupting the functioning of a biophysical system is a rapid invasion outbreak. Stages of the invasion process pass beyond the framework of the evolutionarily established regulatory principles in a short time interval and, therefore, can have a devastating effect. The feedback principle in biocybernetics leads to a scenario in which the rapid outbreak stage is followed by the effect of a deep crisis, both for an aggressive invader and its biophysical environment. A local population can die. Other sudden crises are provoked by an incorrectly regulated algorithm for influencing populations that are valuable for the economy. In this study, a previously discussed method for organizing hybrid computational structures on the basis of differential equations is developed. The events of switching the forms of equations are found by calculating auxiliary biophysical indicators that specify the moments of redefinitions for changing the stages of the investigated process. An advanced version of a hybrid structure and model scenarios for the collapse effect are presented. Logical errors in estimating the nonlinear dynamics with expert regulation of the impact on a biophysical system are demonstrated. Using an alternative set of predicates, a simulation analysis of launching an invasive outbreak of the population for a dangerous alien invader violating biophysical equilibrium is carried out. The scenario singles out the invasion stages at which measures for controlling an alien species are efficient before an active invader destroyed the environmental resources like Lymantria dispar invasion in Canada.