Game Theory and Applications: Game-theoretic Models in by Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon

By Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon Petrosjan

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The Solution Method of theBiological Kinetics Equation The biological kinetics equations are solved via digitization based on the implicit central difference scheme. The resulting grid equations admit the matrix representation A Differential Game Model of Preventing Fish Kills in Shallow Waterbodies Ax  f 43 (8) where A is a linear positive definite operator (A > 0). To find the solution of the problem (8), apply the implicit iterative process [2] B x m1  x m  m1  Ax m  f . (9) Equation (9) has the following notation: m is iteration number, τ > 0 means the iterative parameter and B designates some invertible operator (a preconditioner or stabilizer).

Volume 17 ISBN: 978-1-63483-489-6 Editor: V. Mazalov, D. Novikov, G. Ougolnitsky et al. © 2015 Nova Science Publishers, Inc. Chapter 3 A DIFFERENTIAL GAME MODEL OF PREVENTING FISH KILLS IN SHALLOW WATERBODIES Alexander E. Chistyakov, Alla V. Nikitina, Guennady A. Ougolnitsky, Maxim V. Puchkin, Ilya S. Semenov, Alexander I. Sukhinov and Anatoly B. Usov Southern Federal University, Rostov-on-Don, Russian Federation ABSTRACT The paper is dedicated to the design and analysis of a differential game model of preventing fish kills in shallow waterbodies.

Example 3. There are 4 projects with the parameters described by Table 17. The number of directions equals 2. The Principle of Coordinated Planning in Control … 27 Table 17. i ai 1 1 2 3 12 6 9 4 6 8 2 4 3 a i2 ci 3 4 Set b1 = 10, b2 = 8, and B = 30. According to Table 17, projects 2 and 3 are multipurpose. Figure 2 shows the network representation of the associated constraints. Figure 2. For instance, take s21 = s22 = 1, s31 = 1, and s32 = 3. This leads to two estimation problems for each direction.

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