Application of Lotka–Volterra Equations for Homeostatic Response to an Ionizing Radiation Stressor

Abstract

Every living organism is a physical, complex system which can be modeled by nonlinear dynamical equations in some very narrowed cases. Here we discuss the adoption and potential application of Lotka–Volterra equations (with damping) to simulate, on a very general level, an organism’s response to a dose of ionizing radiation. The step-by-step calculations show how such modeling can be applied to practically every living thing affected by some external stressor. It is presented that Lotka–Volterra prey–predator equations can successfully model the homeostasis (equilibrium) state of the living matter, with balance between detrimental and beneficial factors which interact in the system. It was shown that too large of a radiation dose can break the damping process, making the system unstable, which is analogous to the irreversible transformation of the irradiated cell/organism. On the contrary, too low of a radiation dose makes the damping factor slightly negative, which means that some nonzero low level of ionizing radiation is the most optimal for an organism’s homeostasis.