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Table of Contents
Intro
Preface
Contents
Contributors
Active Objects and the Higgs Field in the Quark-Gluon Model of Fractal Systems
1 Introduction
2 Description of Active Objects Based on the Quark-Gluon Model
3 Effective Cabibo Angles and Vibrational Modes
4 Heavy Quarks and the Higgs Boson
5 Conclusions
References
Influence of Variable Amplitude and Modulation of the Fractal Index on the States of the Deformation Field of Coupled Structures
1 Introduction
2 Qubit States of the Deformation Field of the Separate Fractal Structure
3 Coupled Fractal Structures Consisting of Two Circular Cylinders with Shifted Centers
4 Conclusions
References
Orbital Waves and Quantum Densities from Time-Discrete Chaotic Sequences
1 Introduction
2 Chaotic/turbulent Flow or Harmonic Type Densities
3 Orbital Sequences in 2d
4 Orbital Sequences in 3d
5 Dense Core Pattern and Surrounding Orbital Pattern
6 Eigenstates with Quantum Symmetries
7 Spontaneous Orbital Collapses and Regenerations
8 Discussion
9 Conclusion
References
Changes in the Rock Mass Geomechanical Properties with Account of the Chaos Theory Based on a Computational Experiment
1 Introduction
2 Substantiating the Main Provisions for Solving the Geomechanical Task to Ensure the Stability of Intermediate Drifts
3 Substantiating the Geomechanical Model of the Behaviour of the Coal-Bearing Mass Surrounding the Intermediate Drift
4 Analysis of the Stress-Strain State of the Rock Mass Surrounding the Intermediate Drift
5 Conclusions
References
Effects of Frustrated Interactions on Synchronicity in Electrical Power Grids
1 Introduction
2 Numerical Methods
3 Results and Discussion
4 Conclusion
References
Chaotic Properties of New 1-D and 2-D Maps
1 Introduction
2 The Proposed 1-D, 2-D Maps
2.1 New 1-D Discrete Time System
2.2 New 2-D Discrete Time System
3 Chaotic Properties Analysis
3.1 Bifurcation Analysis
3.2 Lyapunov Exponents Analysis
3.3 Sensitivity Analysis
3.4 Key Space Analysis
4 Conclusion
References
Transformation of Master-Slave Systems with Harmonic Terms for Improved Stability in Numerical Continuation
1 Introduction
2 Embedding Approach for Bifurcation Analysis and Numerical Continuation
3 Analysis of the LRC-Shunted JJ System
3.1 Model equations
3.2 Cartesian Embedding-Generalized Representation
3.3 Bifurcation Analysis
4 Discussion and Conclusion
References
One-Dimensional Map Without Fixed Points and with Amplitude Control
1 Introduction
2 Vertigo-2 Map
2.1 Fixed Points Analysis
3 Dynamical Behavior
4 Amplitude Control
4.1 Amplitude Diagram and Lyapunov Exponents
5 Conclusions
References
Preface
Contents
Contributors
Active Objects and the Higgs Field in the Quark-Gluon Model of Fractal Systems
1 Introduction
2 Description of Active Objects Based on the Quark-Gluon Model
3 Effective Cabibo Angles and Vibrational Modes
4 Heavy Quarks and the Higgs Boson
5 Conclusions
References
Influence of Variable Amplitude and Modulation of the Fractal Index on the States of the Deformation Field of Coupled Structures
1 Introduction
2 Qubit States of the Deformation Field of the Separate Fractal Structure
3 Coupled Fractal Structures Consisting of Two Circular Cylinders with Shifted Centers
4 Conclusions
References
Orbital Waves and Quantum Densities from Time-Discrete Chaotic Sequences
1 Introduction
2 Chaotic/turbulent Flow or Harmonic Type Densities
3 Orbital Sequences in 2d
4 Orbital Sequences in 3d
5 Dense Core Pattern and Surrounding Orbital Pattern
6 Eigenstates with Quantum Symmetries
7 Spontaneous Orbital Collapses and Regenerations
8 Discussion
9 Conclusion
References
Changes in the Rock Mass Geomechanical Properties with Account of the Chaos Theory Based on a Computational Experiment
1 Introduction
2 Substantiating the Main Provisions for Solving the Geomechanical Task to Ensure the Stability of Intermediate Drifts
3 Substantiating the Geomechanical Model of the Behaviour of the Coal-Bearing Mass Surrounding the Intermediate Drift
4 Analysis of the Stress-Strain State of the Rock Mass Surrounding the Intermediate Drift
5 Conclusions
References
Effects of Frustrated Interactions on Synchronicity in Electrical Power Grids
1 Introduction
2 Numerical Methods
3 Results and Discussion
4 Conclusion
References
Chaotic Properties of New 1-D and 2-D Maps
1 Introduction
2 The Proposed 1-D, 2-D Maps
2.1 New 1-D Discrete Time System
2.2 New 2-D Discrete Time System
3 Chaotic Properties Analysis
3.1 Bifurcation Analysis
3.2 Lyapunov Exponents Analysis
3.3 Sensitivity Analysis
3.4 Key Space Analysis
4 Conclusion
References
Transformation of Master-Slave Systems with Harmonic Terms for Improved Stability in Numerical Continuation
1 Introduction
2 Embedding Approach for Bifurcation Analysis and Numerical Continuation
3 Analysis of the LRC-Shunted JJ System
3.1 Model equations
3.2 Cartesian Embedding-Generalized Representation
3.3 Bifurcation Analysis
4 Discussion and Conclusion
References
One-Dimensional Map Without Fixed Points and with Amplitude Control
1 Introduction
2 Vertigo-2 Map
2.1 Fixed Points Analysis
3 Dynamical Behavior
4 Amplitude Control
4.1 Amplitude Diagram and Lyapunov Exponents
5 Conclusions
References