Advances in Dynamical Systems and Control

1. Front Matter

   Pages i-xxii

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2. Applied Methods of Modern Algebra and Analysis

   1. Front Matter

      Pages 1-1

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   2. Convergence Almost Everywhere of Orthorecursive Expansions in Functional Systems

      • Vladimir V. Galatenko, Taras P. Lukashenko, Victor A. Sadovnichiy

      Pages 3-11

   3. Billiard Systems as the Models for the Rigid Body Dynamics

      • Victoria V. Fokicheva, Anatoly T. Fomenko

      Pages 13-33

   4. Uniform Global Attractors for Nonautonomous Evolution Inclusions

      • Mikhail Z. Zgurovsky, Pavlo O. Kasyanov

      Pages 35-42

   5. Minimal Networks: A Review

      • Alexander O. Ivanov, Alexey A. Tuzhilin

      Pages 43-80

   6. Generalized Pisot Numbers and Matrix Decomposition

      • Nikolai M. Dobrovol’skii, Nikolai N. Dobrovolsky, Irina N. Balaba, Irina Yu. Rebrova, Dmitrii K. Sobolev, Valentina N. Soboleva

      Pages 81-140

   7. On the Periodicity of Continued Fractions in Hyperelliptic Fields

      • Gleb V. Fedorov

      Pages 141-157

   8. Method of Resolving Functions for the Differential-Difference Pursuit Game for Different-Inertia Objects

      • Lesia V. Baranovska

      Pages 159-176

3. Discrete and Continuous Dynamical Systems

   1. Front Matter

      Pages 177-177

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   2. Characterization of Pullback Attractors for Multivalued Nonautonomous Dynamical Systems

      • Jacson Simsen, José Valero

      Pages 179-195

   3. Global Attractors for Discontinuous Dynamical Systems with Multi-valued Impulsive Perturbations

      • Oleksiy V. Kapustyan, Iryna V. Romaniuk

      Pages 197-210

   4. A Random Model for Immune Response to Virus in Fluctuating Environments

      • Yusuke Asai, Tomás Caraballo, Xiaoying Han, Peter E. Kloeden

      Pages 211-225

   5. Some Aspects Concerning the Dynamics of Stochastic Chemostats

      • Tomás Caraballo, María J. Garrido-Atienza, Javier López-de-la-Cruz

      Pages 227-246

   6. Higher-Order Allen–Cahn Models with Logarithmic Nonlinear Terms

      • Laurence Cherfils, Alain Miranville, Shuiran Peng

      Pages 247-263

   7. Uniform Global Attractor for Nonautonomous Reaction–Diffusion Equations with Carathéodory’s Nonlinearity

      • Nataliia V. Gorban, Liliia S. Paliichuk

      Pages 265-272

   8. Some Problems Connected with the Thue–Morse and Fibonacci Sequences

      • Francisco Balibrea

      Pages 273-293

   9. Existence of Chaos in a Restricted Oligopoly Model with Investment Periods

      • Jose S. Cánovas

      Pages 295-314

4. Fundamental and Computational Mechanics

   1. Front Matter

      Pages 315-315

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   2. Two Thermodynamic Laws as the Forth and the Fifth Integral Postulates of Continuum Mechanics

      • Boris E. Pobedria, Dimitri V. Georgievskii

      Pages 317-325

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.



 

• Discrete dynamical systems
• Continuous dynamical systems
• Fundamental mechanics in engineering
• Computational mechanics in engineering
• Optimization for engineering
• Control for engineering
• Decision making for engineering

• Lomonosov Moscow State University, Moscow, Russia

  Victor A. Sadovnichiy

• Kyiv Polytechnic Institute, National Technical University of Ukraine, Kiev, Ukraine

  Mikhail Z. Zgurovsky

Viktor A. Sadovnichiy, Lomonosov Moscow State University, Russia; Michael Z. Zgurovsky, National Technical University of Ukraine "Kiev Polytechnic Institute", Ukraine.

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