Periodic and quasiperiodic control processes in the biocommunity species composition preserving problem

• Main Authors: Alexandra Ivanova, Alexander Kirillov
• Format: Article
• Language: English
• Published: Karelian Research Centre of the Russian Academy of Sciences 2015-10-01
• Series: Transactions of the Karelian Research Centre of the Russian Academy of Sciences
• Subjects: control; species composition; variable structure; periodic process
• Online Access: http://journals.krc.karelia.ru/index.php/mathem/article/view/148

The dynamical model describing several stages of interaction between populations of predators and preys in some area is proposed. The transition from one stage to another is determined by the values of the function which has the sense of trophical attractiveness of a species area. Under condition that the trophical attractiveness not less than threshold value the interaction of populations is desribed by the Volterra--Lotka system. Oterwise, the predator population transfers to a migration stage. The model also describes the process of colonization of the area by predators. The problem of species composition preserving by selection is solved. The selection intensity is considered as a control function. The control which permits to coordinate the anthropogenic impact with natural development of a biocommunity is constructed. As a result, the control process acquires the periodic or quasiperiodic nature which depends on the initial values of populations size. The proposed model is described by the three dimensional system of ordinary differential equations with variable structure.<p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">The qualitative analysis of the system is carried out.</p>