Numerical research of stability in Lotka-Volterra systems with perturbed right side - Альджаафрех, Мохаммад Ракан Абед Алнаби (Technology audit and production reserves, 2014)
The basic effects and patterns that characterize the model of coexistence of two species with weak sinusoidal external effect on the reproduction rate are considered. Solving Lotka-Volterra differential equations describes the ecosystem behavior. Numerical solutions for exposure frequencies, close to the frequency of an unperturbed system cycle are found. The stability of such a non-autonomous system is studied. It is determined that the periodic effect on the population, for example, by changing nutrition or hunting leads to a non-periodic system dynamics. Various forms of irregular behavior of “predators” and “victims” appear in the phase patterns for similar perturbations. All this confirms that even relatively simple models of ecosystems reveal their instability, i.e., sensitivity to small external perturbations. The parameters of perturbations, leading in the proximity of resonant perturbation to both non-periodic growth of populations and non-periodic motions over a finite area, or to stabilization around zero, are defined. Herewith, extinction of populations is quite possible. The obtained results can be used by experts in the field of ecology and economy.