Nonlinear Dynamics, Chaos, and Complexity: In Memory of Professor Valentin Afraimovich

Preface
Contents
Professor Valentin Afraimovich
The Need for More Integration Between Machine Learning and Neuroscience
1 Introduction
2 Machine Learning and Neuroscience
3 Multilayer Adaptive Networks in Neuronal Processing
4 More Innate Structure in Machine Learning Algorithms
5 Conclusion and Outlook
References
Quasiperiodic Route to Transient Chaos in Vibroimpact System
1 Introduction
2 The Reason for Studying of Quasiperiodic Route to Chaos
2.1 The Initial Equations. Loading Curves and Amplitude-Frequency Response
2.2 Neimark-Sacker Bifurcations
3 Discontinuous Bifurcations
3.1 Discontinuous Bifurcations Under Excitation Amplitude Varying
3.2 Discontinuous Bifurcations Under Excitation Frequency Varying
4 Lyapunov Exponents
4.1 The Largest Lyapunov Exponent Calculation
4.2 The Comparison of Different Estimations
5 Quasiperiodic Route to Chaos
5.1 The Whole Motion Picture at Frequency Range 7.45 rad cdot s-1leqωleq8.0 rad cdot s-1
5.2 Oscillatory Regimes at Frequency Range 7.45 rad cdot s-1leqωleq8.0 rad cdot s-1
6 Conclusions
References
Modeling Ensembles of Nonlinear Dynamic Systems in Ultrawideband Active Wireless Direct Chaotic Networks
1 Introduction
2 Historical Background
3 Problem Statement and Modeling Scheme
4 Ultrawideband Direct Chaotic Active Network
4.1 Direct Chaotic Transceiver
4.2 Network Node
4.3 Organization and Operation of UWB Network
5 Modeling Continuous-Time Systems
5.1 Kuramoto Model
5.2 Emulation of Kuramoto Model on the Active Wireless Network
5.3 Computer Simulation
6 Experiments with Network
6.1 System Dynamics in the Absence of Couplings
6.2 Dynamic Chaotic Mode
6.3 Equilibrium State
6.4 Synchronization
6.5 Destruction of the Couplings
7 Limits of Modeling on Active Wireless Networks
8 Conclusions
References
Verification of Biomedical Processes with Anomalous Diffusion, Transport and Interaction of Species
1 Introduction
2 The Preservation of the Nonnegativity of the Solution of the System of Parabolic Equations
3 Auxiliary Results
References
Chaos-Based Communication Using Isochronal Synchronization: Considerations About the Synchronization Manifold
1 Introduction
2 Chaos-Based Communication and Coupling Schemes for Isochronal Synchronization
2.1 Delayed Coupling and Delayed Self-coupling
2.2 Injection Locking and Mutual Delayed Coupling
2.3 Delayed Bidirectional Chain Coupling
2.4 Mutual Delayed Coupling and Direct Self-feedback
3 Discussion
4 Final Remarks
References
A Sequential Order of Periodic Motions in a 1-Dimensional, Time-Delay, Dynamical System
1 Introduction
2 Methodology
3 Implicit Discretization Scheme
4 Period-m Motions and Stability
5 Sequential Periodic Motions
6 Numerical Illustrations
7 Conclusions
References
On the Geometric Approach to Transformations of the Coordinates of Inertial Frames of Reference
1 Introduction
2 Statement of the problem
3 Isotropy
4 Inverse transformation
5 Transitivity
6 Conclusion
References
Corpuscular Models of Information Transfer in a Random Environment
1 Introduction
2 Concept of Random Media
3 The Shift-Randomization
4 Importance in Quasistationary Environment
5 Stochastic Importance in Random Environment
6 Gaussian (Normal) Environment
7 A Homogeneous Medium with Inclusions of Finite Sizes
8 Poisson's Model of Point Inclusions
9 Inhomogeneous Randomized Poisson Model
10 Field, Generated by Poissonian Point Ensemble
11 Stratified Random Environment of Markov Type
12 Phason Interpretation of Markovian Medium
13 Stratified Random Medium of the Renewal Type
References
Kinetic Equation for Systems with Resonant Captures and Scatterings
1 Introduction
2 Resonant Phenomena in Slow-Fast Hamiltonian Systems
3 Evolution of the Distribution Function
References
Solvability in the Sense of Sequences for Some Non-Fredholm Operators in Higher Dimensions
1 Introduction
2 Solvability in the Sense of Sequences with Two Potentials
3 Solvability in the Sense of Sequences with Laplacian and a Single Potential
References