Advances in Dynamical Systems and Control

Description

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.   Front Matter....Pages i-xxii Front Matter....Pages 1-1 Convergence Almost Everywhere of Orthorecursive Expansions in Functional Systems....Pages 3-11 Billiard Systems as the Models for the Rigid Body Dynamics....Pages 13-33 Uniform Global Attractors for Nonautonomous Evolution Inclusions....Pages 35-42 Minimal Networks: A Review....Pages 43-80 Generalized Pisot Numbers and Matrix Decomposition....Pages 81-140 On the Periodicity of Continued Fractions in Hyperelliptic Fields....Pages 141-157 Method of Resolving Functions for the Differential-Difference Pursuit Game for Different-Inertia Objects....Pages 159-176 Front Matter....Pages 177-177 Characterization of Pullback Attractors for Multivalued Nonautonomous Dynamical Systems....Pages 179-195 Global Attractors for Discontinuous Dynamical Systems with Multi-valued Impulsive Perturbations....Pages 197-210 A Random Model for Immune Response to Virus in Fluctuating Environments....Pages 211-225 Some Aspects Concerning the Dynamics of Stochastic Chemostats....Pages 227-246 Higher-Order Allen–Cahn Models with Logarithmic Nonlinear Terms....Pages 247-263 Uniform Global Attractor for Nonautonomous Reaction–Diffusion Equations with Carathéodory’s Nonlinearity....Pages 265-272 Some Problems Connected with the Thue–Morse and Fibonacci Sequences....Pages 273-293 Existence of Chaos in a Restricted Oligopoly Model with Investment Periods....Pages 295-314 Front Matter....Pages 315-315 Two Thermodynamic Laws as the Forth and the Fifth Integral Postulates of Continuum Mechanics....Pages 317-325 Flow Control Near a Square Prism with the Help of Frontal Flat Plates....Pages 327-350 Long-Time Behavior of State Functions for Badyko Models....Pages 351-359 Front Matter....Pages 361-361 Adaptive Control of Impulse Processes in Complex Systems Cognitive Maps with Multirate Coordinates Sampling....Pages 363-374 Estimation of Consistency of Fuzzy Pairwise Comparison Matrices using a Defuzzification Method....Pages 375-386 Front Matter....Pages 361-361 Approximate Optimal Control for Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions and General Quadratic Quality Criterion....Pages 387-401 On Approximate Regulator in Linear-Quadratic Problem with Distributed Control and Rapidly Oscillating Parameters....Pages 403-415 The Optimal Control Problem with Minimum Energy for One Nonlocal Distributed System....Pages 417-427 ....Pages 429-471