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Foreword; Contents; Part I Nonlinear Dynamics
Fundamentals; On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles; 1 Introduction; 2 Canonical Dissipative Nambu Systems; 3 Four-Dimensional Canonical Dissipative Nambu Systems with Limit Cycles; 3.1 Construction of Closed Curves in Four Dimensions; 3.2 Canonical Dissipative Nambu System with a Single Limit Cycle; 3.3 CD Nambu System with Several Limit Cycles; 4 Conclusion; References; On the Dynamics of Chaotic Systems with Multiple Attractors: A Case Study; 1 Introduction; 2 Description and Analysis of the Model
2.1 The Model2.2 Dissipation and Existence of Attractors; 3 Numerical Study; 3.1 Numerical Methods; 3.2 Route to Chaos; 3.3 Occurrence of Multiple Attractors; 4 The Analog Computer Approach; 5 Concluding Remarks; References; Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation ; 1 Introduction. Short Outlook of Singlevaluedness and Multivaluedness in Nature and in Models; 2 Strong Anticipation Property; 3 Examples of Investigated Problems with Anticipation; 3.1 Two-Step Discrete-Time Anticipatory Models
3.2 Logistic Equation with Strong Anticipation 3.3 Cellular Automata with Anticipation; 3.4 The ``Game of Life'' as an Example of a Cellular Automaton; 3.5 Neural Networks with Anticipation; 3.6 Boundary Value Problems with Anticipatory Boundary Conditions; 4 Possible Properties of Solutions and Further Research Problems in Physics; 4.1 Multivaluedness and Self-Organization; 4.2 General Distributed Media with Anticipation; 4.3 Oscillators and Chimeras and in Media with Memory, Nonlocality and Anticipation. New Research Possibilities; 4.4 Chimera States in Systems with Strong Anticipation
4.5 Possible Research of Physical Systems5 Possible Ambiguity in the Theory of Computing Machines and Computer Architecture; 5.1 Possible Development of the Theory of Cellular Automata; 5.2 Problem of the Reconstruction of Concepts; 6 Interpretation of Mental Reactions and the Problem of Consciousness; 6.1 Property of Anticipation (Foresight) in Theory and Nature; 6.2 The Possible Role of Strong Anticipation in Thinking; 7 Uncertainty and Probability; 8 Conclusion; References; Part II Nonlinear Dynamics
Selected Applications
Nonlinear Modeling of Continuous-Wave Spin Detection Using Oscillator-Based ESR-on-a-Chip Sensors1 Motivation; 2 Introduction: Oscillator-Based Spin Detection; 3 Magnetic-Energy-Based Modeling of the Spin-Induced Inductance Change in Continuous-Wave Oscillator-Based Spin-Detection Experiments; 4 Phase and Frequency Noise in LC Tank Oscillators; 4.1 Preliminary Considerations; 4.2 Nonlinear Oscillator Modeling; 4.3 Nonlinear Oscillator Modeling in the Presence of Noise; 4.4 A Model for the Phase Noise in LC Tank Oscillators Based on a Special Case of Bogoliubov's Asymptotic Method
Fundamentals; On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles; 1 Introduction; 2 Canonical Dissipative Nambu Systems; 3 Four-Dimensional Canonical Dissipative Nambu Systems with Limit Cycles; 3.1 Construction of Closed Curves in Four Dimensions; 3.2 Canonical Dissipative Nambu System with a Single Limit Cycle; 3.3 CD Nambu System with Several Limit Cycles; 4 Conclusion; References; On the Dynamics of Chaotic Systems with Multiple Attractors: A Case Study; 1 Introduction; 2 Description and Analysis of the Model
2.1 The Model2.2 Dissipation and Existence of Attractors; 3 Numerical Study; 3.1 Numerical Methods; 3.2 Route to Chaos; 3.3 Occurrence of Multiple Attractors; 4 The Analog Computer Approach; 5 Concluding Remarks; References; Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation ; 1 Introduction. Short Outlook of Singlevaluedness and Multivaluedness in Nature and in Models; 2 Strong Anticipation Property; 3 Examples of Investigated Problems with Anticipation; 3.1 Two-Step Discrete-Time Anticipatory Models
3.2 Logistic Equation with Strong Anticipation 3.3 Cellular Automata with Anticipation; 3.4 The ``Game of Life'' as an Example of a Cellular Automaton; 3.5 Neural Networks with Anticipation; 3.6 Boundary Value Problems with Anticipatory Boundary Conditions; 4 Possible Properties of Solutions and Further Research Problems in Physics; 4.1 Multivaluedness and Self-Organization; 4.2 General Distributed Media with Anticipation; 4.3 Oscillators and Chimeras and in Media with Memory, Nonlocality and Anticipation. New Research Possibilities; 4.4 Chimera States in Systems with Strong Anticipation
4.5 Possible Research of Physical Systems5 Possible Ambiguity in the Theory of Computing Machines and Computer Architecture; 5.1 Possible Development of the Theory of Cellular Automata; 5.2 Problem of the Reconstruction of Concepts; 6 Interpretation of Mental Reactions and the Problem of Consciousness; 6.1 Property of Anticipation (Foresight) in Theory and Nature; 6.2 The Possible Role of Strong Anticipation in Thinking; 7 Uncertainty and Probability; 8 Conclusion; References; Part II Nonlinear Dynamics
Selected Applications
Nonlinear Modeling of Continuous-Wave Spin Detection Using Oscillator-Based ESR-on-a-Chip Sensors1 Motivation; 2 Introduction: Oscillator-Based Spin Detection; 3 Magnetic-Energy-Based Modeling of the Spin-Induced Inductance Change in Continuous-Wave Oscillator-Based Spin-Detection Experiments; 4 Phase and Frequency Noise in LC Tank Oscillators; 4.1 Preliminary Considerations; 4.2 Nonlinear Oscillator Modeling; 4.3 Nonlinear Oscillator Modeling in the Presence of Noise; 4.4 A Model for the Phase Noise in LC Tank Oscillators Based on a Special Case of Bogoliubov's Asymptotic Method