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The model of Collision Prevention System (CPS) is verbally defined on the basis of the appliance of sailing and maneuvering regulations COLREGs -72[1]. For the control of ships passing process it is possible to use two methods: 1) classical, that is a directive method of control; and 2) non-classical, or individualized control being exercised through interactions among a group of ships – active systems (AS) in the homogeneous environment. The first so called classical method shall be used in accordance with all the rules (except item (b), Rule 2, Responsibility). Within this context the main objective is to be achieved by means of control actions being of extremely directive effect similar to «elementary prohibition». The main principle of decision-making will be rule-oriented method linking fuzzy linguistic variables. A set of the rules define the strategy to control a ship for preventing collisions at sea in ordinary circumstances and characterized as «ordinary practice of seamen». Non-classical control methods cover everything that can ensure a safe sailing of ships in the event of immediate danger of collision between ships in compliance with «good seamanship», i.e. item (b) Rule 2 to be applied.

Because of a conflict arisen from a dangerous approach of ships they have to continuously solve the problems of finding for a new safe condition taking into account both classical and non-classical methods of control and consequently the transition of AS from dangerous condition to a new balanced safe condition (figure 1).

Figure 1. Transition from balanced into unbalanced condition and vice versa  

In the catastrophe theory [2] such development of the situation is called «bifurcation». On the figure 2 it is demonstrated a family of evolutionary processes with one-dimensional phase space (on abscissa axis it is indicated a parameter value  – the closest point of approach; on ordinate axis – COLREG condition-). Collision may occur provided the parameters of approach get into so-called «bifurcation area» [2], i.e. area of a close-quarters situation or/and critical change of ship’s operational parameters. These parameters may be distinguished as external (geometric arrangement of ships relative to each other, their lengths, speeds, etc.) and internal (engine oil pressure, temperature of exhaust gases, etc). Based on this concept a situation taken from the point of bifurcation might have development in different ways: a ship might either be lost or sustain considerable damages or it might return to its original track and proceed with its normal operation in the previous mode. This situation is shown on the figure 3. If the main external criteria of a ship’s safety – closest point of approach   and time of the closest point of approach ( change intermittently and their parameters of approach are within allowable limits of the safety area, the ships will pass «clear». Provided that the parameters change more or less than allowable values  the ship will get into a dangerous area (area of immediate danger of collision) which is shown as crosshatched region on the figure 3.

Figure 3. Parameters of ships’ collisions in bifurcation area

Figure 3 is to be clarified as follows:

1) Bifurcation fold (1) takes place in the safety area. Such change of parameters of ships approaching will correspond to the concept of «ordinary practice of seamen».

2) Fold (2) takes place in the dangerous area; however, actions taken by navigators in compliance with «good seamanship» have enabled to ensure the safety of   a ship according to 2 Rule, Responsibility, by making a departure from COLREGs-72.

3) The parameters of the fold (3) are those characterizing parameters of an accident or wreck as a result of collision

Taking into account the above mentioned a collision of ship can be analytically defined as follows:


This definition has a simple interpretation – collision occurs when parameters involving safe condition of a ship go beyond the limits of the safety area ( as a result of conflict for the period of time ΔT < Tall, necessary for taking immediate actions to prevent the danger of collision between ships.  The functional «property» of a ship to counteract the threats arisen involves control actions to be developed in order to prevent or mitigate the unwanted consequences.

In any case for the purpose of ensuring safety the functioning of a ship has to be involved with a necessity of response to the counteracting forces and consequently the given «bifurcation» of safety parameters shall be taken into account when making decision and selection of ships passing strategy.  Thus, fold types (1), (2) or (3) enable to resolve the uncertainty in selecting the strategy of ships passing in compliance with COLREGs-72, i.e. classical or non-classical method of ships passing control to be applied.


  1. International Regulations for Preventing Collisions at Sea 1972 (COLREGs-72) // Consolidated edition. – 2002.
  2. Arnold V.I. Catastrophe Theory // 3rd Berlin Springer-Verlag. — 1992.
    In the present paper the safety of ships passing is based on the premise that a ships passing is associated with a conflict function. Formalized description of such a conflict is given in terms of the catastrophe theory as a gradual or intermittent change of control parameters of a stable ship’s motion enabling to determine the appropriate ships passing strategy.
    Written by: Astrein Vadim Viktorovich, Shtyrkhunova Natalia Aleksandrovna
    Date Published: 01/04/2017
    Edition: euroasia-science.ru_29-30.12.2015_12(21)
    Available in: Ebook