New Perspectives on Nonlinear Dynamics and Complexity (Nonlinear Systems and Complexity, 35)

✍ Scribed by Dimitri Volchenkov (editor), Albert C. J. Luo (editor)

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 198
• Category: Library

✦ Synopsis

This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.

✦ Table of Contents

Preface
Contents
1 Offset Boosting Regulated Multistablity
1.1 Introduction
1.2 Implementation of Offset Boosting
1.3 Regulating Multistability by the Hidden Offset
1.3.1 Trigonometry Function
1.3.2 Absolute Value Function
1.4 Discussion and Conclusion
References
2 A Further Analysis of the Passive Compass-Gait Bipedal Robot and Its Period-Doubling Route to Chaos
2.1 Introduction
2.2 The Passive-Dynamics Compass-Gait Biped Robot
2.2.1 Description of the Biped Robot
2.2.2 Dynamic Model of the Passive Bipedal Walking
2.2.2.1 Swing Dynamics
2.2.2.2 Impact Dynamics and Impact Conditions
2.2.2.3 Complete Model: Impulsive Hybrid Dynamics
2.3 Determination of Period-1 Fixed Point
2.4 Influence of the Slope Angle of the Walking Surface φ
2.5 Influence of the Length a of the Lower-Leg Segment
2.6 Conclusion and Future Works
References
3 Hidden Attractors of Jerk Equation-Based Dynamical Systems
3.1 Introduction
3.2 Leonov's Analytic-Numerical Localization Method
3.3 Hidden Attractors in Jerk Systems
3.3.1 Two-Part PWL Jerk System
3.3.2 Three-Part PWL Jerk System
3.3.2.1 Stable xe1,e3 and Unstable xe2
3.3.2.2 Stable xe2 and Unstable xe1,e3
3.3.2.3 Stable xe1,e3 and xe2
3.3.2.4 Unstable xe1,e3 and xe2
3.4 Closing Remarks
References
4 Analysis of a Hyperchaotic System with a Hyperbolic Sinusoidal Nonlinearity and Its Application to Area Exploration Using Multiple Autonomous Robots
4.1 Introduction
4.2 The System
4.3 Application to Chaotic Area Exploration
4.3.1 Robot Dynamics
4.3.2 Coverage
4.4 Conclusions
References
5 3D Nonlinear Flow-Induced Vibration Model of Tubing Strings in High-Pressure, High-Temperature, and High-Yield Curved Gas Wells
5.1 Introduction
5.2 3D Flow-Induced Nonlinear Vibration Model of Tubing String
5.2.1 Vibration Control Equation of 3D Tubing String
5.2.2 Load Analysis
5.2.3 Solution Scheme
5.2.4 Experimental Verification
5.3 Results and Discussions
5.4 Conclusions
References
6 From Radiation and Space Exploration to the Fractional Calculus
6.1 Historical Touch. Mathematical Context. Definitions
6.2 Some New Mathematical Scenarios Related to Classical and Quantum Mechanics
6.3 The Solar Radiation and the Atmospheric Dust. Martian Planetary Boundary Layer. Fractional Calculus Modeling
6.3.1 Foundations of the Propagation of a Radiation in a Medium: Attenuation of the Radiation
6.3.2 Foundations of the Propagation of a Radiation in a Medium: Relevance of the Aerosol Optical Thickness
6.3.3 Present and Future Work in Dust and Solar Radiation Diffusion
6.4 Electromagnetic Waves. Fractal Structures and Metamaterials
6.4.1 Metamaterials
References
7 Design of a Multi-System Chaotic Path Planner for an Autonomous Mobile Robot
7.1 Introduction
7.2 Chaotic Path Planning Generator
7.2.1 Logistic Map
7.2.2 FitzHugh–Nagumo Memristive System
7.2.3 Proposed Sampling Method
7.2.4 Motion in 4 Directions
7.2.4.1 Memory-Free Method
7.2.4.2 Memory Method
7.3 Motion in 8 Directions
7.3.1 Memory-Free Method
7.3.2 Memory Method
7.3.3 Statistical Analysis
7.4 Conclusions
References
8 Double-Frequency Jitter Influence on Synchronous States of Time-Delayed Oscillator Networks
8.1 Introduction
8.2 OWMS Chain Network Model
8.3 Double-Frequency Jitter Amplitude
8.4 Simulation Results
8.5 Conclusion
References
9 Hölder Continuous Fractal Interpolation Functions
9.1 Introduction
9.2 Preliminary Results
9.3 Uniqueness of Invariance in an Essential and Broad Sense
9.4 A Certain Class of FIFs
9.5 Conclusions
References
10 Solvability in the Sense of Sequences for Some Non-Fredholm Operators Related to the Double Scale Anomalous Diffusion in Higher Dimensions
10.1 Introduction
10.2 Solvability in the Sense of Sequences with Two Potentials
10.3 Solvability in the Sense of Sequences with Laplacian and a Single Potential
References
11 Uncertainty in Epidemic Models Based on a Three-Sided Coin
11.1 Factors of Pandemic Uncertainty
11.2 A Biased Three-Sided Coin: Susceptible–Infected–Immune
11.3 Decomposition of Entropy into Predictable and Unpredictable Information Components
11.4 Fractional Transition Times on Condition of Self-quarantine
11.5 Exacerbating Uncertainty with Vaccination and Self-quarantine Restrictions
11.6 Conclusion
References
12 The Energy of Trees with Diameter Five Under Given Conditions
12.1 Introduction
12.2 Preliminaries
12.3 Main Result
References
Index