Modeling of Transformations of Biophysical Processes in the Caspian Sea by Wave Equations with Perturbed Delay

Abstract

This study is devoted to computational analysis of nonlinear biophysical processes with adaptation of methods of analysis of relaxational oscillations from the arsenal of models in technical physics. The method of computational modeling is developed with a modification of hybrid wave equations for biophysical processes with staging and critical transformation events, in which complex sporadic transient oscillations and wave fronts are generated abruptly. The prediction of spreading of alien organisms in a new environment is a topical problem in modern biophysical cybernetics. The processes occurring after the invasion of an alien biological agent with an extremely high reproductive potential for the new medium activate confrontation with mutual evolutionary adaptation of parties. New equations with delay are proposed for modeling the variants of development of oscillatory regimes in biological systems. During the invasion of a new species, the effect of destructive burst of population develops, which can be prolonged in time and space. Models have been constructed with account of the uncertainty factor in the rate of generation of the response to the intrusion of a dangerous species; however, the perturbation in this case is quite limited and does not actually lead to a stochastic dynamics of the biophysical process in autochthonous surroundings and alien intruder. The models presented here exhibit different behaviors with the emergence of bifurcations and cycles with different properties. The existence of nonlinear effects with a randomization of trajectories is contradictory. Iterative models often generate undesirable nonlinear regimes of the behavior in the prediction of the dynamics of invasive processes with account for a regulating action. The hybrid models a life cycle with evolution stages developed here fit into the proposed criteria of essential interpretation in biophysics and prediction of invasive processes in marine biosystems, which is typical of intrusions in the basin of the southern part of the Caspian sea at the Iran and Azerbaijan costs. The processes of change in the composition of fauna during the period of stagnation of the river runoff and expansion of invasive effects investigated here include an intricate complex of varying nonlinear dependences. We propose a computational algorithm as a predicatively redefinable trigger structure of equations with a hybrid representation of time, which are analyzed using scenarios in the representation of the computational scenario with a set of parameters, initial values, and the algorithm of the expert decision making concerning the change of action on the population. Using computational experiments, the actual scenario is described, which leads the biological system of a collapse with a controllable level of action; this is illustrated by the example of degradation of a unique biota of the Caspian Sea during the disturbance of the optimal hydrophysical situation and fresh water runoff of the Volga and Kura rivers. It is shown that the main reasons for the Caspian biota collapse are associated with systematic errors in the control of fishery in 1980s. The absence of stringent mathematical principles of catch of sturgeon has led to the threat of fish kill because of the disregard of the concept of the critical biomass of the population. The reason for the collapse were the predatory exploitation of bioresources, overestimation of the abundance of populations, erroneous methods of catch quoting, and overstated rate of population restoration by the release of artificially cultured baby fishes. The hybrid structures is relevant for many discontinuous processes in biophysics.