Abstract <p>The article is devoted to the development of computational models for special transformations of biophysical processes based on the construction of variable structure of hybrid models according to the principles of the physical theory of phase transitions. The article develops a methodology for modeling rapid phenomena, such as population collapse, based on bifurcation theory in the phase space of hybrid discrete-continuous systems. We will consider several important situations with nonlinear effects in the development of ecological processes in aquatic and terrestrial biosystems. Our models for the accumulation of biogenic elements were built based on empirical dependencies. Computational structures for population dynamics can be built based on differential equations or iterative structures with different time steps. There are some situations where it is necessary to introduce discontinuity into the model and several ways to make jump changes to a model. The new models allow obtaining complex transient oscillation regimes. We proposed the new method with the definition of a set of conditions for rebuilding equations, the construction of a&#xa0;computational structure using the forms of continuous-event time, and the logic of the redefined behavior of solutions to the system of equations due to external interference to describe one of the practically important options for the development of extreme events in the management of biological resources. As a result of expert control of inflated data on the state of the sea biosystem, the impact exceeds the optimal level. Expert control in the model is set by a system of logical functions. Making a management decision based on incorrect assumptions has a cardinal impact on the risk of collapse. Because of the intervention, the stable state of the biosystem is destroyed, and the managed stocks pass into a state of oscillations. In the oscillation mode, the impact does not correspond to the level of population reproduction. We propose simulating erroneous decisions and risky regulatory options in scenario-based experiments. In the computational scenario, a collapse situation develops after transient oscillation regimes which can no longer be prevented by a moratorium on the impact. The dynamic scenario of crisis has been implemented for the stocks of bottom aquatic organisms and differs from the previously considered model scenarios. It is not possible to improve this situation for studying bioresources after an event of collapse. The use of the model can be extended to other collapses of fish stocks in the Black and Caspian seas, when fish stocks were affected by the invasion of harmful ctenophores. The results of this study are applicable across a broad range of biophysical research for the model-based analysis of complex phenomena. A scenario-based approach is proposed to describe prolonged crises, rapid collapses of valuable bioresources, hazardous invasions, and pulsating epidemic processes. The primary objective of this ongoing research is to formalize the overarching mathematical concept of structural ecodynamics. This framework of new structural ecodynamics theory entails classifying of the forms of behavioral options for components of a hybrid model solution and transformation pathways in biosystems and correlating these events with bifurcation patterns and rearrangements of attractor basin boundaries in the hybrid systems.</p>