By Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon Petrosjan
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Additional resources for Game Theory and Applications: Game-theoretic Models in Mathematical Ecology
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  B x m1 x m m1 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.