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DOI: 10.15507/0236-2910.026.201601.020-031
ALTERNATE PURSUIT WITH THREE PARTICIPANTS (THE CASE OF POINTWISE MEETING)
Viktor Shiryayev (professor of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya St., Saransk, Russia), Ph.D. (Physics and Mathematics), docent, ORCID: http://orcid. org/0000-0003-0497-3769, This email address is being protected from spambots. You need JavaScript enabled to view it.)
Yekaterina Anoshchenkova (senior lecturer of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya St., Saransk, Russia), ORCID: http://orcid.org/0000-0001-7256-6634, This email address is being protected from spambots. You need JavaScript enabled to view it.)
Ravilya Bikmurzina (associate professor of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya St., Saransk, Russia), Ph.D. (Pedagogy), ORCID: http://orcid.org/0000-0002-7651-6340, This email address is being protected from spambots. You need JavaScript enabled to view it.)
The issues connected with alternate pursuit of escapees group are considered in a number of papers. So in papers [1–3] the solution of the problem has been found in the assumption that the next meeting is selected at the initial time (by the program) and the players are moving straight. In paper [4] the solution of the task using the approach of R. Isaacs is given. In paper [5] the choice opportunities of the next meeting ( both software and positional) are considered. The article deals with a simple differential game on the pursuer plane P and the coalition of two escapees E={E1,E2}.The movement of all the players are assumed as inertialess. The pursuer speed P exceeds the speed of each of the escapees. The targets, physical abilities and the exact location of each other in any moment of the game are known to all players. The price of the coalition (the pursuer P) is (minus) the total time spent by the pursuer P on the pointwise meeting with E1 and E2 . A coincidence of pursuer and escapee location is meant under the meeting. The choice at the initial time of the persecution is supposed as given (software selectable regular meeting). The limit of the security zone of the second escapee has been found. A geometric approach is used in the problem solving. The resulting system of equations is solved numerically by means of computer algebra, in particular through the Wolfram Mathematics. After defining the boundary of the second escapee security zone one can study the game between the pursuer Р and three escapees acting in concord (the first escapee is eliminated from the game).
Keywords: simple persecution, generally parallel convergence, circle of Apollonius, security zone, coalition, strategy
For citation: Shiryayev VD, Anoshchenkova YeV, Bikmurzina RR. Alternate pursuit with three participants (the case of pointwise meeting). Vestnik Mordovskogo universiteta = Mordovia University Bulletin. 2016; 1(26):20-31. doi: 10.15507/0236-2910.026.201601.020-031
This work is licensed under a Creative Commons Attribution 4.0 License.
