Overview:
This book surveys modern progress in nonlinear dynamics, combining analytical, numerical, and AI-driven methods. It covers fractional and stochastic models, qualitative dynamics like chaos and bifurcation, and machine learning tools such as PINNs for PDEs. Beyond theory, it explores applications in physics and cosmology, including graph theory, black hole dynamics, and wave propagation in curved space-times. By uniting classical analysis with computational intelligence, the book presents a comprehensive perspective on complex systems across science and engineering.
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🔍 Book Scope and Features:
• Advanced analytical and numerical techniques for solving NLPDEs
• AI-driven approaches and Physics-Informed Neural Networks (PINNs)
• Applications to astrophysical systems, including black holes and cosmology
• Graph-theoretic and topological approaches in modeling complex dynamics
• Nonlinear stability, bifurcation, chaos, and stochastic behavior
• Integration of machine learning in scientific discovery and modeling
• Applications to biomechanics
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📖 Proposed Sections and Topics
• Numerical and Analytical Methods for Nonlinear PDEs
• Fractional and Stochastic Modeling in Nonlinear System
• Lie Symmetry Analysis and Invariant Solutions
• Qualitative Dynamics: Stability, Bifurcation, Chaos, and Modulation Instability
• Machine Learning in Nonlinear System Identification
• Physics-Informed Neural Networks (PINNs) for PDEs
• Computational Intelligence and Optimization Algorithms
• Topological Descriptors of Chemical Networks
• Mathematical Models in Cosmological Evolution
• Stability and Dynamics of Black Hole Solutions
• Soliton and Wave Propagation in Curved Spacetimes
• Nonlinear Field Equations in Relativistic Settings
• Mathematical Modeling of biofluids
• Intelligent Modeling using hybrid structure of fuzzy graphs
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📘 Editors
Dr. Miguel Vivas-Cortez, Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Católica del Ecuador Sede Quito, Ecuador.
📧 mjvivas@puce.edu.ec.
* Dr. Dean Chou, Department of Biomedical Engineering, National Cheng Kung University, Tainan 701401, Taiwan
📧 dean@gs.ncku.edu.tw
Chapter Proposal Submission:
Please submit an abstract no longer than 500 words at pristbook76@gmail.com by July 25, 2025.
Key Features:
1. Professional review, editing.
2. Professional cover-page design and typesetting.
3. ISBN number
4. Online publication of the book.
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📆 Important Dates
• Submission of Abstracts: 25 July 2025
• Acceptance of Abstracts: : 27 July 2025
• Chapter submission deadline: 15 August 2025 to
• Review Process: 15 August 2025 to 7 September 2025
• Acceptance notification: 8 September 2025
• Publication date: 15 September 2025.
